Ask individual hotels whether you can be put onto a wait list for a room. Be sure to mention if you would be willing to take a room for only part of the conference and switch hotels if necessary.

Watch availability on the computer yourself, when logged into your account (in case the hotel releases a guaranteed availability room). Don't count on your travel agent to do this as diligently as you would like, and don't count on the hotel giving any last minute rooms to people on the waitlist (if they permit a waitlist).

IME, some conferences will help even after the deadline for hotel arrangements. Ask them nicely.