I've been looking into this (thanks for the pointer to Sensitronics!), do you have any pointers to a manufacturer of squishy material pads? (silicone I guess)
Sensitronics was recommended to me by Roger Linn one time I met him when he happened to be in town for an event. They apparently make the sensor in the Linnstrument.
What I do is I glue a sheet of 1/8th inch birch ply to a sheet of felt using liquid hide glue, then use a laser cutter to cut that into keys. (They're irregular polygons, but you could do the same easily with squares.) I have another piece of laser cut plywood (or the "negative space" of the same plywood, but with the felt removed) that serves as a frame to hold the keys in place. I use packing tape on the back of the frame, sticky side up, to grab onto the felt so they don't all fall out when you turn it upside-down. The felt gives the keys a satisfying squishy feel. Wood screws hold it all together.
In other words, from top to bottom a key is comprised of 1/8th inch birch ply, a layer of glue, a layer of felt, a layer of tape sticky side up, a layer of FSR film, then ENIG-coated copper traces on an FR4 PCB with the solder mask excluded. I also have another layer of plywood (1/4") on the bottom for structure.
I made an early attempt at using some kind of silicone rubber, but I wasn't successful. It might be doable and I imagine there are companies that can make that stuff for you but in the end I decided I liked wooden keys better and they were just plain easier.
I don't have leds on the keys, but if you want that, WS2812's are surprisingly cheap and could be placed by a pick-and-place machine by the hundreds -- if you can figure out a way to get the light to shine through all the intervening opaque parts.