You're probably correct that to first order, the function of the thwarts is to maintain a shape.
Without them, the boat will spread out if supported only (or only close to) the centerline. Support in the water will be more evenly spread up to the waterline, and that probably will reduce the gap.
If the existing boards are preserved well enough to determine their lengths, I would go with that value. I read somewhere (on this forum most likely) that they may have been individually sized for each boat (to make up for variation in manufacture). Because of that being a very real possibility, I would always aim to reproduce the actual parts as much as possible.
That said, I don't think being off some small fraction of an inch is going to be critical --- as long as it doesn't result in the CB being put under an
asymmetric side load.
Mine are 12 3/4 and 12 7/8, and from the difference you can see that the CB isn't located symmetrically between the seats. It's only about 1/8 (or perhaps 3/16, measurement was pretty rough) of a difference, but it is a difference. So, if you can copy the existing parts, that would be best (and you can stop overthinking at that point
)
Otherwise, if their length has been "lost", take your best guess but do it in plywood, and then you can disconnect them once in the water and see whether (a) they are overall to long/short and/or (b) whether one side should be made a bit longer/shorter than the other. When satisfied, you can cut the part from expensive wood. (But I wouldn't go that route, if you can copy the old parts).
As they are simple parts, they would respond well to being epoxy sealed (as long as you seal the holes as well). By excluding moisture, you prevent the wood from working, and any varnish (or PU) that you put on will last a lot longer (it won't crack from expanding wood). I've had good success with SystemThree's clear WR-LPU for this application (over 2-3 coats of laminating epoxy, like SystemThree's SilverTip -- they also sell ClearCoat, while it spreads more easily, it doesn't build as much, and for this kind of application a thicker coating seems preferable to me). Just always be sure to keep the epoxy coated with something that has UV inhibitors in it.
You may need to fill the holes in the seats with something, as the wood backing may be well-rotted as well. Overdrilling the hole, scraping out additional rotted wood, then filling with fiberglass cloth strips and soaking them in epoxy would create "plugs" into which you should be able to drill new holes (or into which, before hardening, you should be able to screw your screws after waxing them, so you can remove them later - the curing epoxy will form threads around them).
Filled (thickened) epoxy does not work for this purpose. It's not strong enough on the short scale needed to hold onto the threads for your screw; unlike glass fibers, the fillers interfere.