Re-applying to PhD programs I'm reapplying to one school I got rejected from and it's my top choice. Is there any chance they just might go like "oh, him again?" and throw it out or something, or not read it?

My application is going to be very different and, in my opinion, much stronger this time, with 2 new pieces of research.
Short answer: No.

Long answer: If it is a good university, they will repeat the whole process, regardless of previous applications, even more if the application is different. It is possible that they consider the result of the previous judgment to see if anything changed, but I don't  think that is that likely..

The members of the committee itself may have changed as well. Unless you have the mother of all red-flags on your CV, that would make you unbelievably memorable, you are probably safe...