OK I'm Avionics but I have been doing this for a while and I have never come across warm up as a method of increasing EGT margin. You don't mention which P&W but both JT8 and JT9 seem to benifit from a compressor wash. Don't remember doing them on JT3s
A previous company used to do regular, scheduled, washes on JT8s.
While CFM56s, V2500s, and especially CF6s all seem to benifit so it might be an idea.