The it would be worth approaching companys like ICI or Brown Brothers or autopaint international who make the paint and asking their advice, if no success then it might be worth re-painting the entire booth, this might be the cheapest alternative, the problem with this type of procedure is that it souns like a variety of paints that have been used, and to clean it up would be a very difficult job as achieving good results without stainage would be difficult.
Slightly off the subject we restored a 1972 mercedes 3.5 litre V8 and fully stripped down paintwork it took a lot of effort with an orbital sander and even in places a little nitromors that should give you an idea of how hard it can be especially if the booth is quite old, if it is a newish booth without any scratches chips etc in the panels then it might not be to bad however you must still check that no damage will come to the booth as a result of heavy powerwashing, it might be worth doing a sample pane first before entering into a contract and notify the client of the possible risks
regards Dave Adl