I used to have a pop top on a Catalina
many years ago. I didn't have that problem but my suggestion is to take it off, pop it the other way (convex) and reinforce your wood planks (beams) by adding about a half inch thickness to each of them. I hope these planks as you describe are running athwartships? You can cut strips of wood any species you want that is thin enough to bend in the direction you desire. Once you have about enough strips to add that half inch, then mix up some epoxy
and microfibers and glue them in place using copper or bronze nails or stainless staples and weights to keep them stable until the epoxy
goes off. You can do all that while your pop top is upside down on your lawn or at the dock
A word of caution - tape off everything that you don't want smeared with epoxy!!
The other option is to add more athwartships beams.
The reason for the problem is that you don't have the cabin
sides helping to hold the pop top in the proper shape when crew weight is placed there.
Another suggestion would be take it off, pop it the right direction, but it back on and epoxy and glass it in permanently. If you like the pop top feature then that option is out.
I added a tie down feature on my pop top because I took the boat to sea and didn't want it popping open at the wrong time, if you catch my drift?
Hope this helps a little.