booth - I'm not currently an EDB NET but will be applying for the scheme this year, same as you. I have been working as a NET (but not through EDB) for the last yr and a bit... Last year I was too late for EDB deadline, this year I only worked part time because I'm doing an MA. I am similar to you in that I don't have a PGDE, just a degree (soon an MA in linguistics which might help) and a CELTA. (but also over two year's experience in HK which might help)
I agree with you that it is very hard to make 38k freelancing, unless you're running your own business or have cheap access to a classroom and a large supply of students. I am tempted to go that route though, fully aware that it won't be as easy - but should be more rewarding in the end. Also, I'm thinking of going nito working at a university (again the salary would be lower at first but it fits in better with my preference for a career path)
Anyway - going back to the point - yes you can apply to schools directly and if they are looking for a govt NET they can help with the procedure and pretty much guarantee you a place, provided you passed the interview etc.
I'm applying for the NET scheme as a backup... I hope I won't need to use it even if I'm accepted!
Quite a rambling post - Make of it what you will - I'm off to teach!