Before installing the beadboard I put a coat of semi-gloss acrylic latex paint (good grade household interior paint) on the front and back of all the boards. Once that dried, I picked up a few tubes of construction adhesive from the local hardware store and got to work. A note on construction adhesives: there are so many different types I had trouble making a decision. I hope what I chose will work; it's a general adhesive that should bond wood to multiple surface types so I'll cross my fingers.
The process for installing all the boards was simple. Lay each one down backside facing up and run a wavy pattern of adhesive along the back and then press into place. Repeat until done. I ended up using just 1 of the 3 tubes I purchased. It was way easier than I thought it would be and didn't run into a single snag. I had blocked off 2 hours of time to get it done, but found it only took about 30 minutes, so I ended up putting another coat of paint on before I left.
After letting it set up overnight, I came back the next day and use a few pieces of paper to template the section around the chainplate bolts for a piece of mahogany. I didn't want to put the beadboard there, because the soft wood would crush under the tightened down chainplate bolts. I took the template back to the shop and cut out another piece of the old coamings and planed it down to 5/8". I traced out the template pattern and cut out the shape on the wood with a jig saw.
I headed back to the boat with a rasp and the new chainplate board (I don't know what to call it) and after a bit of filing away, I had the board fitting nice and snug. I screwed the rest of the trim (I still have a few small pieces left to make) and was happy to see that everything fit quite nicely. Of course all the trim had to come off to get sanded and the first of several coats of satin varnish (I'm just using Helmsman Urethane for the interior) before final install, but it's looking more done than not now.
So given that both bulkheads are almost identical in size, I can estimate now that for each bulkhead the cost breakdown is as follows: $14 per package of beadboard (used just shy of 1 package), $3 for each tube of construction adhesive (used 1), and $3 for a box of 25 3/4" stainless steel #6 screws (will be enough for both sides). This brings my grand total for each side to about $18.50. Of course, I had free trim mahogany so if I had needed to purchase it, I would say it would have probably doubled the price, but still one of the cheaper boat projects I can think of.