Took me almost two hours to write this up, but with my limited experience with various VR titles I think I figured out the most intuitive and precise controls possible for TTS on the Vive.
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Firstly:

Fix the laser:
The laser currently implemented works great for games with guns, but when just trying to point at an object or a menu item pointing it straight forward like a remote control (or the SteamVR System Menu) just feels more natural.

Fix the teleport system:
Currently whenever I try to use it I just stay where I am. I don't know if it's because TTS had an update or SteamVR or what, but I can't teleport around the room at all anymore. Also, adding the option for in-game locomotion (not by default) will make some users that don't like the teleport system happier, making it feel more like an actual game room.

Switching between Laser and Hand Controls:
Rather than trying to gauge the weird proximity required to activate hand mode when playing simply make it so 1 button (the grip button) switches easily between laser pointer mode and hand-grip mode. In addition, make the hand-grip mode actually look like a hand (or glove) facing the same way your actual hand is facing. The best example of this I can think of is Job Simulator. It's silly, but it works.

In hand-grip mode while holding an object your virtual hand disappears to allow you to see the object you're holdin. The only exception will be the touchpad buttons which appear while your thumb is currently touching, but not clicking, the touchpad. This will allow you to see the object completely, but still see the touchpad options at will.
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Main Menu:
Shrink it down and bring it a bit closer to the player's face so it's easier to read, or make it scaleable same as in-game for table/room. Maybe make it a pinup board like you see in game shops sometimes. Other than that it's pretty good, actually. Allow scrolling via the pointer touchpad when selecting games. Make it so the only button on the touchpad that shows is the teleport button because there are no objects to shuffle/rotate/flip/interact with in any way. Allow users to teleport closer to the menu wall to read it better.
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In-Game Controls:

Not holding or pointing at anything unlocked:
- Grip button - switch between laser pointer and direct hand interaction, same as when you're currently holding/lasering an object. This should be its ONLY FUNCTION. That super zoom thing should be saved for objects you are already holding (I'll get to that).
- Lower touchpad button - scaling (currently handled by grip buttons). If you're not holding or pointing at anything, the flip button is functionally useless anyway. Set this as the scaling button when not pointing or holding anything.
- Center touchpad button - teleport/movement direction controller facing (only along X/Z axis, does not change height) (alternative locomotion option toggleable in options menu along with movement speed)
- Left and right touchpad buttons - Nothing (technically rotate, same as current, but nothing is selected or hovered over so it does nothing).
- Upper touchpad button - In laser mode make this a quick switch key for the Vector or Pixel line draw tools. While holding it down and pulling the trigger it draws things with the laser. In hand mode, switch to a Vector or Pixel pencil/pen/marker/whatever in your virtual hand to physically draw with. OR turns your hand into a giant pencil/pen/marker/whatever that is scaled to the size of your Vive controller, allowing you to grip the controller like an actual writing tool and write with it in-game. Currently if you're not pointing at or holding something this button does diddly, so let's give it a useful function.
- Trigger - grab/select area. Same as current. (If it ain't broke, don't fix it!)
- Menu button - open menu (same as current)

When hovering over object in hand-grip mode:
- Grip button - switch to laser mode.
- Lower touchpad button - flip (same as current)
- Center touchpad button - super zoom (currently handled by grip button while not holding an object). This will allow you to see the object/card at a larger scale without changing the actual scale of it. Useful for small text and requires the player to be close to the object/card to enlarge it, preventing cheaters from peaking at face down cards with the laser (currently do-able with grip buttons and laser)
- Left and right touchpad buttons - rotate (same as current)
- Upper touchpad button - shuffle/roll/etc (same as current)
- Pull trigger - pick up object/stack/single card (same as current)
- Menu button - bring up right click menu and laser (same as current), disable grip button to switch to hand-grip mode while menu is up, switch back to hand-grip mode when pressed again

When pointing at object in laser mode:
- Grip button - switch to hand-grip mode.
- Lower touchpad button - flip (same as current)
- Center touchpad button - nothing.
- Left and right touchpad buttons - rotate (same as current)
- Upper touchpad button - shuffle/roll/etc (same as current)
- Pull trigger - pick up object/stack/single card (same as current)
- Menu button - bring up right click menu (same as current), disable grip button to switch to hand grip mode while menu is up, stay in laser mode when pressed again

When holding something in hand-grip mode (holding trigger):
- Grip button - switch to laser mode. Once object is let go hand switches back to grip mode, or stays in laser mode (toggelable in options)
- Lower touchpad button - flip (same as current)
- Center touchpad button - super zoom (currently handled by grip button while not holding an object). This will allow you to see the object/card at a larger scale without changing the actual scale of it. Useful for small text and requires the player to be holding the object/card to enlarge it, preventing cheaters from peaking at face down cards with the laser (currently do-able with grip buttons and laser).
- Left and right touchpad buttons - rotate (same as current)
- Upper touchpad button - shuffle/roll/etc (same as current)
- Pull trigger of 2nd controller (also in hand-grip mode) within certain proximity of 1st controller object held - grab/set scale of object, as though you are stretching the object to be bigger or squishing it to be smaller. Must reach a certain threshold of stretching before scaling starts to prevent accidental scaling in case of just putting something in other hand. Does not engage if already holding object in 2nd controller (already holding trigger).
- Pull trigger of 2nd controller (also in hand-grip mode) within certain proximity of 1st controller holding multiple objects at once - if pulled quickly will scale whole group of objects. If 2nd controller trigger held, then select object in hand of first controller will be grabbed and grip will transfer from 1st controller to second controller. If 1st controller trigger let go before scaling or gripping of single item triggered, entire stack will be transferred to 2nd hand (still holding trigger).
- Menu button - pick up second object, or any objects touched while menu button held (currently only doable with mouse by pressing right click)

When holding something in laser mode (holding trigger):
- Grip button - switch to hand-grip mode. Once object is let go of switches back to laser mode, or stays in hand-grip mode (toggleable in options)
- Lower touchpad button - flip (same as current)
- Center touchpad button - nothing.
- Left and right touchpad buttons - rotate (same as current)
- Upper touchpad button - shuffle/roll/etc (same as current)
- Pull trigger of 2nd controller while pointing at same object - hold = cut deck in half, pull quickly like drawing card = draw card off top of deck. If holding multiple objects at once pointing the second controller laser at one object in group and holding trigger for a moment will pull selected object from stack of objects same as with regular object on table. If 1st controller trigger let go before single object from stack is removed then entire stack transfers to 2nd controller laser (still holding trigger).
- Menu button - pick up second object (currently only doable with mouse by pressing right click)
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If I missed anything let me know. This would allow (mostly) complete integration of same basic controls available to mouse and keyboard/controller users. Allowing VR users to play with a gamepad (360 or otherwise) instead of the Vive controllers would also allow non-Vive users (such as Oculus or OSVR users) to play in VR, opening up the VR scene to a wider array of players.