Why does my whole print lift the plate off the bed?

Your theory is basically right, and splitting it in half is one legit fix, but there are a few things to try before you go there. What's happening is the bottom layers cool and shrink while everything above them is still warm, so the solid sheet of plastic you've got bonded to the plate has nowhere to go except up. On a part that spans nearly the whole bed, the leverage is huge, so it doesn't just curl the corners, it lifts the plate. ASA is worse about this than PLA or PETG because it shrinks more as it solidifies.

The single biggest thing that worked for me on big flat panels: break up the bottom surface. You can emboss a shallow grid or diagonal pattern into the first couple layers of the model, like 1mm deep lines forming big diamonds or squares. Instead of one giant continuous skin pulling in every direction, you've got a bunch of small sections that each shrink a little on thier own. It also adds a nice grip texture to the lid, wich is a bonus. Same idea applies to infill, and this is where Hilbert curve really earns its keep. It never has a long straight line running edge to edge, so there's no continuous shrink path to the corners. Regular rectilinear infill at 45 degrees basically draws arrows pointing at your corners and tells them to curl.

Also check your infill angle. Rotate it so lines don't run parallel to the edges or shoot straight into them. That alone helped one of my prints go from curled to flat.

Two more things worth trying: give the bottom a couple solid layers then switch the rest to lighter infill, since a 10mm thick part doesn't need to be solid anyway and less material means less total shrink force. And keep the chamber warm but stable, no drafts hitting it mid print. A raft can help too because it acts as a sacrificial buffer that curls instead of the part. If none of that works, yes, split it in two with a stepped joint and glue them. But I'd bet the grid pattern plus Hilbert curve gets you there.

Funny thing I learned on a similar monster part: more grip isn't always the answer. I had corners tearing up my plate until I went the other way, light glue stick coat and a wide brim, so when the pull got too strong the brim tips released instead of the part itself levering up. Ugly edges to clean but the lid came out flat. Have you watched which lets go first on yours, the part or the plate?

Not buying the embossed grid idea honestly. Plastic doesn't care where the little grooves are, it still shrinks as one connected chunk once those layers fuse together, which happens basically instantly. I tried something similar on a big ASA panel last year, cut slots into the bottom, and it curled just the same, only now the corners had a bunch of little seams to telegraph the warp through. What actually helped me was bumping the bed temp up higher than what felt reasonable and letting the whole thing cool slowly with everything closed until it was basically room temp. Rushing the cooldown at the end undoes half the work the warm chamber does during the print.