Okay, so. I nixed the double-sided tape because, of course, I do want to be able to ever undock my tablet. It was actually a bit nerve-wracking, because that tape REALLY held well and I almost couldn't get the tablet out without damaging it.
Next up, I tried those 3M tabs. They worked okay for awhile, but eventually, no matter how I placed them, they'd come loose and I'd get disconnects. It got so bad that I finally decided it was time to give up on the dock entirely.
I had a bluetooth keyboard/touchpad device lying around, so I got creative. The dock still has one thing that I like: the hinge and hook mechanism. I took the dock apart and ripped out all of the guts. I took my bluetooth keyboard/touchpad apart and reduced it to its bare essentials (control board, keyboard, touchpad, buttons, and battery). I carved out bits of the internal structural plastic and shoehorned the keyboard and touchpad in. Yeah, I went there.
Now I have a WORKING keyboard and touchpad in the dock. It still folds up nicely and of course I can dock and undock the tablet to my heart's content. The keyboard and touchpad actually fit surprisingly well in the case, and there are really only a few gaps through which you can see some wires and such. I might just leave it like that because it looks neat
Here's the best part: there's a magnet to the upper right of the touchpad in the dock. I was trying to figure out what it could be for, when it hit me. I moved the dock's bezel over the tablet and poof, the screen went out. Moved it away, and it came back. This is the magnet that triggers the tablet's magnetic switch that tells it that the dock is closed. In other words, despite removing all of the electronics in the dock, the tablet still turns off when it's closed. Epic win.
So, that's pretty much the end of my story here. Asus's dock is garbage, so I hacked it into something that works. I won't be buying an ASUS tablet again, and will probably avoid all of their other gear.
Oh, one more thing. I stopped using this bluetooth keyboard/touchpad because I'd get repeated keys and it'd kill wifi performance. I've since bought a new router with 5ghz, and I'm pretty much going to have to avoid 2.4ghz wifi from now on. Small price to pay, though, especially since I can tether to my phone at 5ghz.