I've had an issue twice now with opportunities for a trip in two or three weeeks but not being able to go due to unavailability of visa appointment slots. The specific cases were trying to get a French visa and a South African visa in London - both have waiting times exceeding a month. The best one can do in this situation is to seemingly keep checking the visa appointments portal every day and hope that someone else cancels and you are lucky enough to get it.
I realize the answer to this may depend on the travel agent and consulate but as a general rule of thumb, can travel agents get an earlier appointment slot compared than individual users? Do they have any tricks that can help in this situation?