Considering the forum threads here with private funded students looking for jobs are becoming more and more common I wouldn't waste my money if I was you. Apply to the ANSPs without an age limit and go for that route. That way you will "only" waste time and a bit of money if you fail. If you go privately you will waste time and a big amount of money if it doesn't work.
Yes it is possible to self fund, but considering how difficult it is when you're with one of the big ones I can't imagine how difficult it is to land a job on your own.
Also if you're worried about your age, if you go down the route of working up to a sponsorship through an assitant post or similar then you'll probably be looking at more time than with the big ANSPs, even when you consider the time of the application process and then waiting for a course start.
Regardless of what you do though, good luck