It's easy to mount APs on false ceilings, and wire runs are even easier since it's all concealed.

Just to get an idea, the instructions for mounting on the ceiling tile should be similar. If you can't get through access, then consider other options that you would mount other things on false ceilings -usually with some form of reinforcing plug that gives additional surface behind the plasterboard.
Far easier to get a good switch and use injectors. You can use multiple port injectors like these (it's a random google image):
https://bigamart.com/product/ws-poe...MIm5LI9dfg9gIV-IJLBR1IUADNEAQYAiABEgKsPPD_BwEOf course, these are always on, so if your device is not PoE capable, it will be very wise not to plug it in after the injector. Just connect those devices direct to switch, and use the injectors only for devices that need PoE.