I dare not hit the quote button again. Too much work to keep breaking all that up.
You should be able to ask any friendly custom kitchen shop to sell you a roll of laminate. That's what I did. Took a few days as they had to order some in for that particular color.
I used MDF for the center braces as well. Like you, I was concerned about warping and MDF should never warp unless it gets saturated. I wasn't worried about swinging it up so weight was not a concern. Maybe not a good choice for you as it would be too heavy to 'comfortably' swing up to the ceiling on a regular basis, but it could be done and could double as a home gym exercise.
I used 3m spray. I "think" it was 3m 90. Probably overkill again but it has the best resistance to moisture. (screen shifting paranoia again)
Like you, I considered glue but also worried about flatness. You can use a brush but spray seemed easier.
