For many of the chain brands, elite status allows for early check in and/or late check out (usually easier from my experiences) so I usually just get a room for evening prior and check in on way home from work and then request late check out of 4p and that accommodates any mid day outcall needs I've had.  

I've seen ads for mid day room rentals but the concept just seems sketchy. So will follow thread for any suggestions that may be useful! Great question btw.

Some hotels have day rates.  I have visited providers who have taken advantage of them!