One thing I would do is simply not panic - I'm guessing chances are good he may not get in this year, but you still have next year to reapply (at least I'm guessing you do). In the meantime, I'd focus on his vision therapy and getting him as much enrichment as you can at his current school for this year - and plan to have him test for the school again next year, when hopefully the vision issues are hopefully resolved, or at least better

In the meantime, if you think he needs accommodations in testing for his vision issues, work toward that at school - you aren't going to ultimately get accommodations for an ability test (that doesn't make sense), but if you do have accommodations in place with a specific plan, you should be able to get those same accommodations for achievement testing for the gifted program next time he's tested. Another thing you might consider after his VT program is over is having him tested privately again, but this time choose a tester who can write a supportive letter for helping him get into the program if the tester feels it would be beneficial. You can't really ask them up front to write that letter - they will need to test them first and then have a sense of what they think he needs, but you can ask them up front if their evaluation will include recommendations for schooling, and once he's tested, if he meets the testing bar, you can ask that they address the specific school situation in their report or request that they write a separate letter.
Re your appeal - I think the first thing I'd do in making the appeal is look at the percentiles they use on cutoffs for the ability tests that they do use - is it 95th? 98th? 99th? Then compare that to your WISC GAI - how close it is? If it's close or above, mention that in your appeal letter.
I am also not sure if the WJ-III you mentioned in your previous post was ability or achievement testing (there are versions of both for the WJ-III). If it's achievement testing, compare the percentile to achievement test scores required (if they use any type of achievement tests).
I'd definitely use what you have from the VT eval and any type of explanatory letter from the VT dr as the reason for your appeal (it's definitely "new" information).
I'd also dig (google) for info on specifics of how vision might impact the tests that he was given through the school that are used to apply for the program. Mention those specifics in your appeal letter.
You've also mentioned in previous posts that you suspect he did not get a strong referral from his primary teacher this year. Is there any other teacher (past school teacher, preschool teacher, piano teacher, anyone) who might write up a referral for him?
That's all I can think of at the moment. Definitely be diplomatic in your letter, but also try to put out of your mind any thoughts such as the program is most likely already full anyway so why bother. Give it your best try, and then if the program is full, it's full for this year and it's out of your hands. OTOH, if you've sent in a diplomatic letter - you'll be in a good place to apply again next year when your ds has had his VT and you have more date.
Good luck!
polarbear