Removing glass from the light pathway would result in the loss of infinity focus unless you can decrease the distance between the lens and sensor "past" infinity. Helicoids, bellows, extension tubes will not be helpful because they increase the distance between the sensor and lens.
I suppose what you mean by "short build" adapter is that it is shorter than usual? Such an adapter would work, but I do not know of any commercially available ones. You would have to grind down an existing adapter or build one from scratch. I'm currently working on converting a lens to EF by replacing the mount with a lens reversal ring. Grinding it down to the correct thickness is much more difficult than it is to type. It would be far easier to just replace the glass in the filter stack during camera conversion.
Some compact cameras inherently focus past infinity, and removing the hot mirror filter would not affect infinity focus. However, the only way to know whether a particular camera will work is to try it.
You could also just use lenses that you already know focus significantly past infinity or that can be adjusted for infinity focus. Adjusting the focus on lenses would be easier than building adapters. It's usually just a matter of locating and loosening a set screw. The best candidates would be third-party lenses that were made for different camera mounts. First-party lenses are likely to not have enough room for adjustment.