It's not impossible, nor nessesarily expensive, given a well-thought-out concept.
You could arrange four aluminum right-angle profiles as guides for the removable box.
If you can get hold of a sheet of teflon or similar slippery material, glue it onto the alu profiles so the box can slide nicely in/out.
Split the ends of those profiles and bend the taps a bit out, so you have some nice lead-in guides, else you'll rip-off the teflon.
Assuming you'll need one in, on out and say.. one send/return, all mono, this can be done with three male jacks, mounted inside a U-shaped profile inside the 8U box. After wiring up, fit a lid on the U-profile to avoid hum and noise.
Fit three femal jacks on the box, arranged to precisely match the males.
One stereo male/female pair can serve as both send and return.
This way your box will have normal connections when used standalone.
You'll need to power the box.. for this some male/female connectors will be needed.
I wouldn't use ordinary jacks for this.. So, what could possibly happen? Well, I just wouldn't like having power on the tip of a jack when sliding the box in, if by chance I forgot to ensure having the rig powered off.
Do not make such a slide-in box to accept ac mains power.
Finally, outfit the box with a couple of standard handles, so it can be man-handled