Hi, welcome to the board, we are predominently UK techs on this board so you might get more replies later when our Stateside friends come on line.
With regard to your services, I can see a market but probably not hugely. There are often requests for models for training courses, and competitions but it's a bit hit and miss. Usually someone will take a model to training who is a friend/family/peer so follow up issues can be monitored, plus it can be easier to work on someone you know when you're starting out and lacking in confidence. Requests only tend to come if that model drops out for any reason, and that can often be last minute so I don't know how that would work with your full time employment.
Competitions wise, I suspect you could be in demand but sadly you can only really do one a day as the competitor would need you for nearly the whole day with prep, application, judging, presentations, etc. I believe some competitors will pay models for their time/accomodation/etc. So not a massively lucrative occupation. There are not many competitions, mostly Nailympics annual, and a few at trade conventions. You might get some further information if you made contact with a local nail school/acadamy (not sure what you call them in the US). They may be able to put you in touch with needy techs.
Good luck with your endeavour, it sounds like you could be really helpful to someone once you can find a route in 
