Hi jaytee, welcome to the forum!
I'm sorry that you had such a crummy experience in your childhood. We started looking for answers about our son for similar reasons - both DH and I were bored out of our skulls in school and wanted to avoid the same for our kiddo. The main concern I had was that if our son already knew everything that was being taught, he would never learn how to learn. I didn't want him to have his first educational challenge in college, like I did, and then think he was really not all that smart after all.
I think we didn't really look at the situation as pushing our child, but rather pushing the school to teach our kid at the appropriate level. All the other kids have a chance to learn perseverance, so why doesn't my kid?
I'm glad the language immersion school is working for now. If you do a search of this site, you can find several threads on how GT kids do in language immersion schools. Some do fine, some do great for a year or two until they figure out the language and realize everything is too easy. It sounds like your son's school is pretty flexible, so maybe they will be willing to do some differentiation or further subject acceleration as necessary. It may also be a good idea to take stock of the GT programs in your area or within driving distance. A lot of times GT kids, even when accelerated, find the pace too slow. Many fulltime GT programs will have a faster pace and also more intellectual peers (plus less need to skip grades).
For us, we found that our kid liked to hide in the classroom. He did not want to stand out, so he didn't often show his abilities. In kindergarten, our DS was testing at least a couple years ahead in math and reading, like your son. The most helpful test was the NWEA MAP test, so the school could see how our kindergartner compared with the 2nd graders, e.g. If your school uses that test, I'd recommend asking for it early (sometimes schools won't give it until 2nd grade). We also had our son privately tested (IQ) before kinder, so we had those reports to back us up too.
Because our kiddo would complain at home about things being boring, but was happy to do the easiest stuff while at school without complaint, we probably seemed like we were pushing when asking for 2nd grade math in kindy and then a skip of 1st grade. It turned out the skip wasn't enough, but the pieces finally fell in place when we transferred to a school for HG kids with an accelerated program (meaning the base level of all subjects was one year ahead, plus they worked faster, so had more time to get into additional units). Since we moved him to this school, we have not had to advocate or push in any way, because we see that he is challenged with the accelerated program along with the grade skip. We put very little emphasis on his grades, as we know he is being challenged (and he's in 4th grade -- grades don't matter anyway). We will revisit your question again when the program ends after 5th grade!
I really don't think it's pushing to advocate for your kid to get the same benefits out of school as most the other kids - learn something new every day; learn to try something, fail, then persevere.
