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I'd use 3M VHB tape. With a little heat from a hair dryer it could be removed again if the table needs to be re-purposed but it would be difficult for the little hoodlums to remove. We use it at work to anchor things when we don't want to drill holes like on the side of anesthesia machines.
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Location: Around Sacramento
When I built my son's table I put a 3/8" lip around the edge. It keeps the plates in place and he can rearrange them as he pleases. He has road, moonscape and plain ones and the table is big enough for a 4x4 (maybe 3x3, I'm not in a spot where I can check) grid of them. Gluing them down would limit his creativity.
One feature I really wish I had included was a hole with a "manhole" cover that could be removed and the Legos bulldozed through the hole into a bucket below. Picking up hundreds of Legos off the table sucks.
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I think Worthing's idea is the way to go. That way the base plates can be swapped out. If they have to be stuck fast then tape would be way better than glue or epoxy IMO. Good luck with the project.
Luke
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By the way this is my Lego table... Built the main body of it when I was 14 or 15. Still in my parent's basement almost 25 years later. Some day I'll have to move it all... That's going to be a moving truck rental my wife won't like
You can crawl under and stand in the middle. It actually has a hinge and clasp so you can open it and walk in (I also broke my leg when I was 14, so crawling wasn't much of an option), but it's way too heavy for that. The little side wings and upper deck were added later
Benny