Good start as Tom says
"I thought was more convenient to use than my previous experiment with cheese glue. "
Because cheese glue is more of a joinery glue for sticking bits of wood together, they used animal sizes, I simply use supermarket gelatine, mixed strong and hot, it does the job beautifully and very cheaply, I do not recommend rabbit skin glue as it is not worth the money when gelatine will do.
I am currently refurbing a limewood one (sorry for the delay JW).
As for the gutter, you can make a simpler and equally proper version by simply lapping the wings under a central plank, you get a shallow gutter but you also reduce the need for any hollowing out. Some were hollowed, a lot were not, or at least not by looking at the real ones, pics or otherwise.
Your covering canvas, should ideally be well washed and quite coarse, some pavises have a coarser canvas on the inside and a slightly finer one on the outer, the gesso is similarly better applied to the front and just enough to fill the grain on the inside, presumably because more gesso means a smoother surface for any painting.
Oak was used, but as you have found is very heavy, other lighter woods include:
Tom can add more.
As for paints, really easy to do in period with a slight adjustment.
1 - animal based glue, make a gelatine solution that is sticky enough to stick your palms together when pressed.
mix this well with the colours of your choice, put the pot over a water bath to keep it fluid. Brush on in thin strokes, it will dry quickly enough.
Then use a polyeurethane GLOSS varnish to seal.
2. Varnish medium
If you want to make proper varnish do it, but you do not need to.
Polyeurethane GLOSS varnish, mixed with the pigments of choice, brush on.
Why gloss? well because that was what they used and prized, for some reason many reenactors think matt is somehow more 'period', the evidence is to the contrary, a gloss effect was desired in not just oil media, but gums were used to add lustre.
You may find that initial coats absorbd and you get some dull patches, that is fine, simply add a coat when the job is dry.
Do be careful of the colours you use, many of our pigments are much cheaper than then, so be as restrictive as you can, suggested colour palette:
vermillion (synthetic from Cornellissen) - medium expensive colour
nickle yellow, a substitute for lead tin yellows, is bright.