The picture of the original keyboard you showed looks an awful lot like an old Cherry keyboard, the same type that the early Tandy Model Is used to use. I've been inside enough of them to be 99% sure since we used to have to take off every keycap on some units and bend one "finger" of the split contact forward to prevent "key bounce".
I probably have a couple of keyboards around in my Tandy parts.
It is very close to the Tandy Model 1, but not 100%. A few keys on the right are missing. See pics below
Well, that particular Model 1 hardly counts - it's been modified with some other keyboard. Probably as a method to get rid of the horrible keyboard bounce the early Model 1's had....
I wasn't thinking of it as an exact replacement, more a place to get the right keyswitches from.
Alternatively, using thin gauge bare wire (28 AWG?), maybe in 14" lengths soldered to each terminal. Then pull the wire through the hole, tighten the slack and solder.
This one. It's what I've had to do when replacing the base on a picture tube. Fortunately, you should only have to do the three switches you replaced, as the factory ones should be fairly easy to align.
But, I wouldn't solder the keyboard on just yet. Get the terminal's logic board working, and verify that all the key positions work (jumper it with a little bit of wire, see if the key registers), that way you know all the tracks are good and nothing else was damaged. You don't want to have to take the keyboard off again to fix a trace underneath it.
So almost all the terminals will have long bare wire hanging from them.
You also need to be really careful that when you solder your extended leads to the board, you don't simultaneously unsolder them from the keyswitch from the heat. Be sure your lengthened terminals are very securely soldered/crimped onto what's left of the old terminals, and to solder quickly to the board.