soix, I've seen many cautions against horizontal stacking but never read any specific reports of damage when doing that. I assume it relates to flatness since humidity or mold could be a problem when stored at any angle.
Apparently your turntable is not set up. So maybe a few visual inspections. If you have any glass tabletops or other absolutely flat surfaces, pull a few LPs from the piles and lay the bare records on top. If there was severe warping or cupping it should be obvious.