Hello MomOf1.. Welcome! I can relate to some of your frustrations in having to wait for the school to do its own testing and delays in getting more appropriate materials for your son.
Not many schools will have experience with highly gifted kids, and it takes a while for the teachers/principals to realize that they are really dealing with someone quite different. I see it as a good sign that the teacher is in regular communication with you and allows you to send chapter books.
"Is it common for people to have to supplement the schools?"
It is fairly common for families who frequent this site. When our DS was in kindergarten, we had him do some online math at home so that he would get something at his level. You may hear the supplementation called "afterschooling". I think that if you are faced with very few school options, afterschooling is a fairly good way to address some portion of the areas that your child's missing in school.
"Is there a way to get the schools to do acceleration by subject instead of grade skips--suggestions or tips on what to say to get it moving faster?" This depends on your school and your advocacy skills. Does your district or school have any official policy on acceleration? Start there, if yes. Many times such policies are posted on the district websites. The Iowa Acceleration Scales are a useful objective tool to determine whether a student is a good candidate for grade or subject acceleration.
IAS description and links on Hoagies I think that sometimes schools have never really thought of subject acceleration. You can start by asking the school about the possibility and whether there are any higher grades that teach the subject matter at the same time as your son's class; that would be the easiest solution.
"Is it common for schools to be so slow on GT? I know TX has lots of education & funding issues but compared to some states this seems horrible..."
It's not so great anywhere, and probably slower before your child hits the usual 3rd grade level. There are pockets of exceptions, but many of us on these boards just learn that we'll have to be advocates from now on.
"Should we pursue the grade skip even though we don't think socially its right? I should add, our son is already the youngest on his campus and is the smallest in his class--2 girls on campus are smaller."
If social reasons are the only reason you don't think a full grade skip is right for you, I recommend going through the IAS yourself too. The social reasons are just one part of the determination of whether a full grade skip is appropriate. Also, it seems that there is quite a range of appropriate social behavior in the next grade up, so unless your child is significantly behind, it's likely he'd fall within the range.
FWIW, my DS7 skipped 1st (Jan. bday) and was one of the smallest in his class before the skip. He's shot up over the summer, but still among the smallest. And now that he's in 3rd, many of the girls tower over all the boys. It doesn't seem to bother DS.
"Do we have to get him under the 504 umbrella with GT in order to get change to occur?"
This will depend on the school district. I have no experience with the 504 process myself.
Good luck to you on your advocacy journey! It gets easier with practice. My advice is to keep the school principal/GT coordinator/teacher on your side as team members in the education of your child. It becomes harder if they get on the defensive. Even though GT stuff doesn't usually start until 3rd, hopefully you can convince the staff that your DS needs services now. We were able to get differentiation from our local school even though GT services didn't usually start until 3rd.