If we expect the Bekenstein bound, or something like it, to hold in a collapsing universe, will that not eventually force us to accept some loss of information, or is there something I'm missing?
Not that I can see. The max entropy S or information I is proportional to RE, radius times energy. Rewrite it as rho/R^2, and as it collapses rho goes to infinity and R to zero. No problem.
Of course it'll become invalid and will have to be described by an unknown quantum gravity before that.
Different in a black hole, all its entropy and information dissappears when it evaporates, thus the still unexplained information paradox. Again, the black hole is really a quantum gravitational object, so you need quantum gravity. The AdS/CFT correspondence has found solutions where the information is not lost, but unless you are willing to do everything via the holographic principle that still doesn't tell us what quantum gravity is.