One of the issues with Catalinas is the size of the companionways - and the bulk of the hatchboards/doors fitted to them.
Hard to tell, but assume those hinges are "lift-off" types? If not that'd be an improvement right off the bat.
I suppose you could have glass/plexi panes and a framed screen that popped in and out, maybe held in with toggle clips or some such.. but it'd be difficult the have such windows be truly weatherproof (makes one of your other objectives hard to reach). We have a solid plexi drop board and a screened one as well - and just use whichever's appropriate. (but our companionway is much smaller, and the dropboards more compact)
Do you have room on the inside of the companionway edges to add another channel for drop boards? They could be wood strips or perhaps an aluminum channel.
btw - the existing ones look pretty nice already!!
1984 Fast/Nicholson 345 "FastForward"
".. there is much you could do at sea with common sense.. and very little you could do without it.."
Capt G E Ericson (from "The Cruel Sea" by Nicholas Monsarrat)