I think that you may be looking at this the wrong way.
Your tripod head is failing you. From your description, it sounds like the manner in which the camera is attached to the head is not all that great. Gimbals are really only used with lenses that have tripod collars, and you may end up spending between $80 to $150 for third party lens collars on eBay that may be of questionable quality. You will of course save the $$ you'd spend on an L Plate for the camera, but you haven't addressed the fundamental issue - a less than optimum tripod head.
The best solution, assuming you have a sturdy tripod, is to get a better head with an Arca-Swiss compatible clamp, and a rail so that you can move the camera back for better balance. Using an L bracket and an Arca-Swiss clamp on the rail to attach the camera will give you the flexibility in switching from portrait to landscape, and keep the camera from rotating. The rail should have a double dovetail so that it can be mounted on the head.
The next best solution is to use a rail on your existing head, but the reality is that if your head is insufficient, the rail will only provide modest benefit.
Hejnar Photo sells quality hardware and I am certain you can put together something with their rails and clamps. See my photos below. I used an 5/8" thick 8" double dovetail rail and a 1-1/2" Arca compatible clamp, mounted crosswise on the rail.
https://www.hejnarphotostore.com/You could go with Bogen/Mafrotto, but it is less of an industry standard and though they have generic L brackets finding a rail that is made to Manfrotto's specs could be a problem. I've never tried looking but you may have better success.
On another note - if you are doing portrait work and you are not doing lots of repetitive headshots, using your camera hand held will provide a lot more flexibility. Using mono lights (preferable) or speedlights lights will keep your images crisp and sharp and free of camera or subject movement induced blur.
I realize none of this is within your budget, but not buying the right gear will only cost you way more than you planned to spend down the road. You already have a tripod and head that isn't cutting it. No point in repeating that mistake.
I think that you may be looking at this the wrong ... (