There are very few non-college aviation schools accredited by the Dept. of Education for Stafford or other federal programs (you mentioned the two that I knew about). There are many commercial companies that make "federally backed" private student loans for aviation schools.
But, there is a huge difference between the two, one is administered by the DOE and provides Grants and small loans, the others are "profit driven" lending institutions (some would say loan sharks) whose loans are backed by the government.
I would not recommend the latter, it wouldn't be wise to put yourself into a lot of rather high interest debt, just to get into a job market that's, shall we say, in a downward spiral
I believe the DOE website has a search function that you can look for aviation schools that are accredited, but of those two the only others I've found were colleges or universities .