As an update, solenoids are now available to order! They work on any xwhatsit Model F or xwhatsit beam spring keyboard! Each solenoid requires a solenoid driver too.
Yes this can be done. There has been some interest and discussion on DT and GH (posts from ~10/7/18). The tough part until now has been finding an available new production solenoid as opposed to buying an old keyboard and pulling the solenoid.
Here is a photo the new xwhatsits with expansion headers preinstalled: https://imgur.com/GyG1wi4
The expansion port also allows for LED lock light mods per xwhatsit’s Model F manual.
Looks like here is one listing for a new production solenoid that some users are confirming compatibility with the Model F xwhatsit solenoid driver: https://www.aliexpress.com/item/DC-6V-0-3A-11W-Actuator-Linear-Push-Solenoid-Electromagnet-w-Base/32267295277.html
One user reported having to trim some material from this product so that it fits in the Model F classic style zinc cases of the IBM F107.
A Deskthority user has added a solenoid to his Brand New Model F Classic Case Keyboard https://deskthority.net/viewtopic.php?f=62&t=23707&p=462600&hilit=f62#p462600