This is sounding pretty good so far. It is not obvious to me that you want to change it. Add in quite a bit of medical experience, strong MCAT test results, and good references, and your chances for medical school acceptance might be better than average.
You are applying to high reaches that take very few transfer students. If you get into any of them, you are going to find that the level of competition in your classes has suddenly ramped up, and you will be competing against students who are used to the tougher rigor.
Either staying where you are or transferring to Rutgers seems to me to be something to very seriously consider. I would add an application to Rutgers while you think this over.
Also, as others have mentioned you should expect to be full pay at UCLA or UCB in the unlikely event that you get accepted. If you want to keep the option open of attending medical school in the future, you should try very hard to avoid debt for your bachelor’s degree. I would not transfer if it is going to add significant debt.
I have a daughter currently studying for a DVM. Years ago she was frustrated by the enthusiasm with which I insisted that she stick to budget. A few years later when she had her B.Sc. in hand she was very glad that I had not allowed her to take on any debt. This is making it easier for her (and us) right now.
Us older folks on CC will sometimes comment on what you want to do without actually answering your question. To answer your question, I would consider all of the schools that you listed as high reaches. To me your applications look more like “prestige hunting” rather than “changing universities to fill an academic need”. This is likely to make transferring more difficult, and it was already going to be very difficult for any of the schools on your list.