Hey whatever, your car. You obviously aren't all that familiar with the product you're planning to use since you're calling people names rather than posting a technical response based on the material properties of the foam. I mean, if there's a reason backed up by material properties why you're not worried about surface adhesion to 40+ year old surface rusted metal and voids that contain drains and built up dirt then by all means share. Instead you just say you're not worried about it and our concerns are laughable? Ok, sure. Your degree in engineering doesn't change the fact that you aren't taking into account that you're not replicating the papers you're using to back up your idea. I didn't even need my BS in aerospace engineering to figure that out. It's right in the papers. The adhesion properties are discussed and pointed out as being the reason why the real life testing didn't match the FEA models in two of the three papers you posted, so the engineers that are familiar with the product and it's application, and did the actual testing, thought it was a worthwhile consideration. But what do they know right?
And yeah, you're not the only one that's seen a torsional rigidity equation. Actually testing the car appropriately to use that equation properly is a different story. Your method will work, but I'm sure you're aware that a single test won't provide you with a margin of error, making it a pretty useless test. You're not going to see massive amounts of deflection measuring the car with the method you're suggesting, so even a small margin in measurement will change your percentages pretty significantly. It's not a bad way to test the torsional resistance if you lack better equipment, but it's not as accurate as other methods either. You'd have to repeat the same measurement at least 10 or so times to give a decent margin of error, assuming the measurements are close.
I'm not trying to preach "fire and brimstone", but your application is different and has issues that need to be addressed before you can just say it's gonna work great. Ignoring those issues could mean the whole operation is useless at best, wasted effort with an added disadvantage of not being able to weld on those areas later without catching the whole mess on fire.
But go ahead, by all means. If you're going to bother testing make sure you get enough data to do some basic margin of error calculations though, otherwise it's just a waste of time. Kind of like the USCT and XV videos. They're neat and all and they show that something happened, but they're not particularly useful for actual data. And unless you test a car that's had frame connectors and torque boxes added to compare to yours you won't really show that adding structural foam is the better way to go, just that it does something. But even the bolt in MP frame connectors do something, so the bar set is pretty low.