Presented for your amusement:
I picked up a P90 magazine from CDNN last year, when they were on sale for $19.95. I bought it just to see how it turned the cartridges 90 degrees to present them to the breech. It uses a nifty helical ramp.
5.7 ammunition is, for some inexplicable reason, dirt cheap now. The "5.7" bullet's published diameters seem to be basically the same as "5.56", so you can use readily-available .223 barrels. You'd have to find a reamer.
As far as the bolt and breech are concerned, the P90 magazine works just like any other magazine.
You could easily build a tube gun, something like the SGN-9 or your own design, that would shoot 5.7x28. The P90 uses straight blowback.
Tube guns tend to range from "industrial" to "fugly" in appearance. If you wanted to make it not quite so industrial looking, you could wrap it in a plastic shell.
Where would you find a plastic shell? I found this FN P90 airsoft:
Amazon.com: Well P-90 Laser Red Dot Airsoft Electric: Sports & Outdoors
It's $26.95, $39 to your door. You could open it up, discard all the airsoft bits, and fabricate some bracketry to wrap it around your tube gun.
I'm not a fan of the P90's looks, though I admit it's rather striking. But as a lefty, the fact that it ejects down instead of my face or left armpit is a strong plus. Also, "cheap is a quality overcoming many faults."