I'd bet with a good model generation, the FEA on this is completely tractable in realtime now. It's only ~2(spokes)*6 dof, and that was doable in a second or so on a sparc in matlab 20 years ago. But to do that, you'd need to be doing beam elements for the spokes and rim segments, not meshing them with smaller solid elements. (And unless you're in non-linear land in material or geometry, a 2 node beam element with 6 dof /node is going to be an exact solution for the spokes, and a good approximate solution for the rim as long as the chord/arc error isn't large. ) And I've found some of the code, and holy crap it's still on the web.
http://www.ce.washington.edu/~soroos/matlab/501/1../wheel2.h... (I'm sure I'm going to hate the 19yr ago me when I dig into that and try to figure out what the hell I was doing based on the comments, because I only remember the outlines of the math at this point. But... I could put this in numpy... I need this like I need another project to suck up my time... And I'm not sure what the me of 2034 is going to think of my code now. But that's another story.)
The real trick with wheels from experience as a wheel builder is that all the really interesting behavior is in the non-linear region. And you're butting right up against that when you lace the wheels tightly. Calculating that limit is tricky.
(Briefly, Ultimate load limit is ~ the sum of the tension in the spokes in the loaded zone of the wheel, roughly 4 or so with the rims/spokes I was looking at at the time. The tension limit is just under what will potato chip buckle the rim. So there's a complex interaction between spoke stiffness, rim lateral stiffness, and rim radial stiffness that affects performance at the load limit. Helpfully, fatigue durability is also better with higher tension in the spokes, since the fatigue performance goes to hell when you get stress reversals.)
FWIW, My masters was investigating back calculating material parameters from a dynamic pavement test based on time histories of surface loading and displacement at known locations. I basically figured out that the error measure that we were using was pretty smooth as the stiffness of the subsurface layers varied and that it was possible to home in on a stiffness profile pretty consistently if there was at least a plausible guess of what was under there. It took a long time then though, overnight runs were common, and we didn't have clusters then. (also, uphill both ways, through the snow) I bet I could do it in near realtime now on my ipad, but that's a masters thesis for someone else.