good luck with getting into DYS! I hope good news is heading your way.
I don't have much to add since we are just starting go down the rapid learning path ourselves but I keep hearing the "don't accelerate too much, you don't want DD at a place where there is nothing left to teach" mantra at school.
I'm also seeing very rapid trajectory of growth in our DD. But like you, DH and I decided against advocating for a grade skipping even though this is what we originally thought was best for DD, simply because they would have to continue to subject accelerate anyway.
I have a question re: singapore math. Do you buy the text books for your DS or just the practice and challenge word problems? I purchased the textbook for DD last summer and I found I didn't need it. TIA.
We went for a skip for social reasons primarily. And we had heard about a 4th grade teacher who had had gifted kids herself so was exactly the right fit at a critical juncture. There was a lot of puerile girly drama that our DD escaped by jumping ahead into a cadre of girls who enjoyed reading some of the books our DD had already read and had already gone through that phase. IMO, a single acceleration will never address our kids' capacity to learn and we ourselves will not be doing another one unless acutely indicated.
Instead, we have taken our DD to kid enrichment activities at a local university ( again for social reasons - and thank God because she finally met a girl like her there) and also we have allowed her to grow her reading and Maths independently.
I have never understood a teacher impeding progress by not letting a kid read whatever the heck they want to read within obvious age-appropriate content driven bounds.
