Akai MK20J tapes for MG1212 12 track

Shells/cartridges, no, those you have to rescue from wherever you can.
Unless you want to pay to have the transport reworked so it will use normal
ordinary Betacam (not Betamax) cartridges for which it was originally designed.
There's a handful of guys that do that, mostly back East.
It's not THAT expensive of a mod and makes life a LOT easier.

Tape that goes inside as well as the leader tape and sensing foil, any ex-VHS/Beta duplicator

Betamax tape is designed for speeds a lot slower than 7-1/2 and 3-3/4 so the best thing apart from adapting say a Fostex half-inch 16 track with a JRF Magnetics 14 track head (12 for music one for sync and one for SMPTE) and recording that way is to use the NON MP or NON-ME tape commonly found in a Betacam.

If you work in TV (mostly cable nowadays) you'll probably have access to all kinds of leftover unused DigiBeta and even though the formulation is wrong and it might be MP tape and therefore abrasive to the 1212 heads (or 1214) you can still get an alright recording on that for effect.

The other thing you can try is the DuPont pure CrO2 12 micron VHS tape that should still be laying around VHS duplicator houses by the pancake-carton-ful. That's about the only tape so far we've been able to find that gives anything even remotely close to a decent recording at 3-3/'4. Being 250 nWm though, the 200 nWm system on
the Akai might record a little weak and/or a little dark, like trying to record a 185 nWm signal on EE reel tape.

Plus, being a little thinner than the normal 14 or 16 micron MK-20 tape, you can get a half hour at 3-3/4 instead of just 20 mins.