Rasmus ports
The Rasmus ports are simple to re-do. The stainless ring around the port is simply screwed in to the fiberglass cabin top. To stop the leak, remove the old window, clean the surfaces, then apply silicone caulk in a continuous bead around the opening. Put your plastic back on, then lightly screw the stainless ring back in place. Let the silicon cure before doing a final tightening. If you tighten it too soon, you'll just squeeze all the caulk out of the gap.
Silicon caulk makes a fine gasket, but is a lousy adhesive - so snugging up that ring is critical. Other caulks (polysulfide or polyurethanes) are better adhesives and sealants - but they tend to attack plastics. If you use 5200, you'll stop the leak, but never get the thing apart again. There is a newer caulk (Lifecaulk maybe - black & yellow tube at Marine stores), that's silicon with a bit of polyurethane. This stuff is wonderful, will form a gasket like silicone, but sticks much better, and doesn't seem to eat plastics like the polysulfides.
If you're re-sealing the ports, you should also look at the shape your windows are in. If they are badly scratched, or show any fracturing on the edges, now's the time to replace them. Use the old panes as patterns, and cut new polycarbonate replacements (same thickness or greater). Some glass stores in yachting regions do this routinely, ask around. A band saw is best for cutting, but I've done this with a saber saw and fine blade. Mask the plastic so the saw base doesn't scratch it up.
You can get tinted material or clear, but try to get something with a scratch resistant coating - and be sure that winds up on the outside.
The common problem is that the screws have stripped out the holes. If that's the case, hunt up larger stainless screws that still match the ring, or fill the old holes with an epoxy / wood mix. Let that harden, the tap new holes. I think the screws mainly engage with the fiberglass and core material, so your damaged wood should not matter too much. The port would be much stronger if you through bolted the ring - but then you'd have to dress up the insides somehow.
Good luck.