Chord length - length of surface interacting with water.
Reynolds number. Ratio of inertia mass to viscosity. Laminar flow breaks down at high Reynolds numbers, but this breakdown is not thought relevant in most surfboard fins.
There are actually people who have created flow tanks and tested water flow around low aspect ratio foils, and this information is available on the web. The flow tank is not so much, maybe 2 feet by 2 feet. With a couple holding tanks and a pump you could do experiments quite cheaply. Just let water go from one tank, down an incline, and into the other. Each run could last a minute or two. Place one fin on a board in the middle, and go from there.
But everything I saw suggested the leading edge vortex theory would be perfectly well supported in the range of Reynolds numbers, aspect ratios, and rake, in surfboards.
IF true, it would suggest that leading edge rake is the most important variable in fin design. Depth is the second. The others fall much further behind (but can have an impact, especially at lower angles of attack where linear (laminar) flow theory dominates ).
Max hold of a fin - simple - as a FIRST APPROXIMATION, it is fin depth. Chord length will have a smaller but not negligible impact.
Drive of a fin, or the increase in lift per degree of angle of attack change. To a first approximation, the leading edge rake. Foiling will have a small/negligible impact at higher angles of attack, and a substantial impact at lower angles of attack.
Stall angle. Dependent principally on leading edge rake - more upright fins stall earlier.
This is all applied assuming infinite stiffness, and a bunch of other stuff. But it meshes well with my own experiences with different fins. Fin rake is highly controlled - 30-35 degrees at the base for almost all thruster fins. For longboards there is a range of 25-30 degrees (interestingly the new Channel Islands Machado singlefin is 35 degree base rake - as though it were made for a quicker board).
And back to the original point. The MVGs, and possibly also the superchargers, may work by more reliably initiating the leading edge vortex, which would increase lift over a limited range of angles of attack (predominantly help initiate it).
I’m thinking about how to go about optimizing a fin for my own system, probably I’ll start with a rake series. And maybe throw the MVGs on the board. 