You might think about leaving the springboard in and just taking out the springs and keeping it closed. Then raise it up with spacers so it's as high as the new connector and that will give the game something to slide in and out on.
Just my two cents.

Also making the perf board as short as possible and then securing it to the back of the Nintendo with 3-4 bolts and nuts would secure it perfectly. And the only obvious modification to the nes would be the 3-4 bolts in the back. But if you keep them small , say size 8 and countersink the heads and maybe even a little gray-white filler and they'd barely be noticeable.
Also if you don't want to buy connectors, just find some cheap game genies and remove their connectors . They work real good.