epictetus, if you make the rods and insert them take pics and let us know step by step how it goes, seems like a 5 dollar solution to a 1 dollar problem, but creativity and DIY spirit are great.
No problem, happy to see my Churchill knowledge of sizes finally was a help. It was strange for me too at first, then I found I needed to use my entire leg and keep my knees straight to get thrust. I found I actually got more thrust from the XL's due to the large surface area. They are floppy though and hard to walk in. The best pair I ever had was a lime green and black colored pair, they were perfectly rigid. The blue and grey pairs always seemed to be floppier. I have never used XL's for bodyboarding but I would imagine the biggest problem would be steering and using the fins as a rudder. There might be some spray on adhesives that you could spray over the fin surface area that would harden them up a bit, rather than trying to add rods. Maybe some stiff hair gel? I am not sure. Maybe If you sprayed them and then stacked some heavy stuff on top to keep them flat?
One thing is for sure your legs might be a little sore from using the XL because they are different, but they will strengthen. Every year when I switched from XL to L or vice-versa I would be sore for about a week.
I worked as an ocean survey swimmer for a few years we swimmers used churchill fins.
So I reinforced one of XLs and tested them out but I still hated them, adding a reinforcing rod along the side helped a little but they were just still really floppy -- I can see how they are good for long-distance swimming but they are not suitable for quick changes of direction / explosive takeoffs (i.e. bodyboarding) in my opinion. A lot of the time when catching a steep wave I may just need to make one single decisive kick which I just can't do very well with the big floppy fins.
Switched back to some other XL fins that came free with my apartment