Welcome to GH
In theory if the switches are good (genuine Cherrys, so unless they're blues they should be) and the PCB works (which it is as the keys work) swapping the controller should fix the problem.
I've never done a TECK but I did mod a Ducky and the principal is the same - you have to map out which switches are connected directly to each other, which diode is for each switch, and which diodes are connected to each other (on the other end from the switch). If you're lucky they use straight rows and columns on a mostly single sided PCB with diodes near the switches so you can see this easily, if you're unlucky it will be like my Ducky which took lots of poking around with a multimeter to work it out.
Once you know how everything's connected you chose convenient places to connect each of the rows/columns to a pin on the Teensy and note which are connected to what.
Probably the most scary part is removing the original controller - I circled a blowtorch lighter round it for a while then heated the middle and knocked it off with a pair of tweezers. Needless to say your expensive new keyboard's warranty will be long gone
)
P.S. Sorry about the CAPTCHA, hope it's gone soon!