OP, I’m in the same boat as you. I’m also an incoming freshman at a top ~30 university looking to transfer to a similar school and I completely understand your reasons. Unfortunately, I have to agree with some of the other posters on this thread about a few things. Transferring to HYPSM is near impossible if you don’t have some type of hook. They want people who don’t have access to the same opportunities that you do. However, what they’re not acknowledging is that other top ~20 schools take a lot of transfers (e.g. UPenn takes over 200). AFAIK, most transfers at non-HYPSM T20’s have no hooks and come from upper-class backgrounds. They likely got in due to high-GPA’s, cool extracurriculars, compelling essays, and the ability to pay. If you absolutely kill it during your first semester of college and get straight-A’s, you’ll probably have a decent chance of getting into at least one top 20 school (USC and Cornell CALS are pretty safe bets).
I’d probably hire a consultant to help with this. It will probably cost ~$10k, but it’s an investment that will benefit you for life. And given your family income, it’s probably not a huge sacrifice. Essays are extremely important when transferring and can make or break you. You need to articulate why you should be accepted and a good consultant will help you come up with a compelling reason.