As to your other questions...
Does this score line up with what you and your DW see in your child? Does it make sense to you given what you know about your child? If so, there's probably no need to retest.
The only other test you might need is an achievement test, since it doesn't appear that he took one, right? DYS usually requests both an IQ and an achievement test, though you could try to apply with a portfolio instead. The worst you're likely to hear is "We need achievement test scores before we can respond yes or no," so you wouldn't be out anything but time.
As for the school situation: all kids--and schools...and teachers...--are different. Some kids do very well in a public school setting, provided appropriate adaptations are made as needed...and all HG+ kids have different needs.
Some HG+ kids just don't do well in public school. Period.
Some schools/teachers just won't bend to suit the needs of an HG+ child.
Flexibility and teamwork from both school and parent seem to be the best keys to whether public school will work or not for an HG+ child. If the school wants to work with you, then it's probably smart to let them. Research your options, of course, but it's hard to beat a free education if it can be made to suit your child's needs.
Some GT programs are very good; some are not sufficient, even when used in conjunction with a grade skip or subject acceleration. You'll have to examine the needs of your child and the actual benefits the program will offer to see if those will line up for him.
I'm sorry if it sounds like I'm not being much help. I'm sure "It depends" is not what you were hoping to hear.
But the fact is that too much depends upon the personality of your child, his interests and specific needs, as well as the actual day-to-day happenings in the classroom. A great teacher can make an HG+ child purr along happily with nothing more than differentiation. A lousy teacher who has a chip on his/her shoulder about GT kids can kill the soul of even the best-laid plans.
One suggestions: if you're considering private and public school, you might also consider homeschooling. No pressure. But it is another option that a number of us have had some success with. If nothing else, it's nice to know about all your options in case you run into trouble down the road.
Welcome to the journey!
I must admit that lately homeschooling comes to my mind as the first solution when kids or parents run into problems in schools. I usually don't say so but it's quite often my first reaction. I guess that's the result of a year of homeschooling