The business of protecting individual power cords was handled by an Eaton PDU that had a 30a twist-lock plug on one side and a couple of rows of current-limited IEC C13 sockets on the other side.
Certainly on my panel the only "single outlet" breakers are hot water, AC, oven/stove, dryer.
Also, another place where you might already have this outlet: some older houses that use window AC units that were larger had 240V 20A outlets. Not common these days, but you can still buy these types of window AC units.
If you're gonna get rewired you may as well install a 240v circuit, and some 120v 20a sockets while you're at it.
I'm very close to just running a cord over or devising a way to put my machine closer to a second circuit because my rental is horribly setup and both my bedroom AC and living room desktop (that also doubles as a ML training box) end up on the same circuit.
It would require an additional run of 14/2G romex (12/2G for 20A) and a single-pole breaker, but allows you to skip cutting in an old work box to add a 2nd duplex receptacle.
You could possibly replace the existing 14/2G with 14/4G which has enough conductors for both circuits.
The receptacle is the easy part, running the new circuit is the hard part.
Or you know, install a new 240V receptacle.
If I have to:
1) Run wire
2) Get a bigger breaker box
3) To do it legally, hire an electrician and maybe get a permit
Replacing the receptacle is like, <1% of what's involved there.
I'm air cooling so I set -pl 450 so I'm not running them all at the full 600w