kinda looks like your coring is shot..... how soft is the wood inside? Any sign of rot/termites...etc?
Couple of options...
First job is getting the part cleaned up and getting all the old adhesive off. I'd personally hit my edges with a soda blaster (just b/c I have one) but a pressure washer and some sanding/wire brushing would probably suffice.
Once you have it clean I'd get a person to help, and a nice cool place out of the sun on a 60-70 degree day. You can also work outside and bring the part inside to cure. If it's too hot/humid the epoxy will cure way to fast.
If the wood is 'ok' then I'd probably turn to west system epoxy thickened with High density filler (404) and Micro fiber adhesive filler (403). I'd probably use a slow hardener as well to give as much working time as possible.
You will need a pastry bag or two like these:
https://www.clcboats.com/shoptips/epoxy_and_fiberglass/e_pastry_bag.html
You've kinda only got one shot at it with the way the part is made, so it may be handy to have 2 or 3 people helping you, with a couple of people just mixing/filling epoxy.
Mix up a small batch of epoxy (un-thickened) and wet out all the surfaces you are going to glue.
Then mix up a couple of bigger batches of thickened epoxy and load into the pastry bags. Squirt a liberal amount of thickened epoxy on the surfaces you want to bond.
After you have a good bead laid sandwich the two parts together and secure them somehow (weights, ratchet straps, couple of screws, whatever it takes to hold them in place for a long time...etc)
DO NOT try to wipe/clean off the epoxy while it's gooey unless you need to mash some into gaps. after a few hours test hardness, once it hardens a little you can scrape your edges with a putty knife and keep everything nice and clean.
Let the part cure for about 24hrs (more if it's colder) and then it should be glued together for life. If any epoxy remains grind it down with the appropriate sanding/grinding tools. The high density filler is pretty damn hard when it's cured so best to get as much cleaned off when it's semi-hard.