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I find that many programs for gifted children that are available outside school do not accept this IQ test for entry into programs. Is there a particular reason? Is it inaccurate? Is it just new? Is it unreliable? I could use some advice and would prefer to avoid private testing if possible.

I find that many programs have different test that they prefer. The RIAS is a certified test and has been standardized, so it is reliable. Every IQ test is different and scores will vary from test to test, some test seem to work better for verbal and others may do better for spacial.
If you are trying to get into a special program I would see if you can submit some work samples, videos of your child, and achievement test results in additon to the RIAS. Achievement testing is usually less expensive and many schoools perform them free. Some gifted programs are pretty strict but others are open to alternatives. My school also uses RIAS and I think it is pretty accurate test. It is better for younger kids because it has a shorter test length so kids don't burn out. Good Luck and Congrats! Those are great scores.