Sticking one USB-C on the front will simplify the spacing in the rear.Why not? It's hardly rocket surgery - I'm sure those very clever people at Apple could work it out. I've got a £20 Raspberry Pi case with two vertically mounted HDMIs - vertical/90º HDMI sockets for mounting on a horizontal PCB are already a thing.
Another possibility is Micro HDMI connectors (as used on the Raspberry Pi - which manages to fit 4xUSB-A, Ethernet, 1xUSB-C, 2 x MicroHDMI and a microSD slot onto something smaller than an Apple TV - and is a real pain for cable management!)
The Studio is built to higher standards than the Mini and a prime example is that it has all of the ports on replaceable, vertically-mounted daughterboards carrying "upward: facing sockets.
The Mini already cheaps out by having a single logic board with directly soldered connectors on the edge - cheaper but mechanically inferior and non-replaceble. If you can get "vertical" HDMI connectors for mounting that way (see above) you can probably get "vertical" USB-C sockets - anyway, Apple will be making tens of thousands (at least) of these things so it would be economical to have them made if they're not available.
Also what about the 3.5mm audio jack that every Mac still seems to have. Perhaps on the front or the side?