MrOptimistic, you definitely should give it a shot! You won't know until you send out those apps.
As for UGPA, if your overall trend is upward, and seems like you have stellar GRE scores and MA work, you can address this in your personal statement/SOP. From my interviews, the PIs I talked to told me that LORs, your personal statement, and having research experiences are important. It's not uncommon to see poor grades in the beginning of college years and improvement later on, and they understand that. You can talk to your LORs and have them back you up in their letters, saying that you are hardworking etc. Although I didn't go through what you went through, but I messed up my first 3 semesters of undergrad (badly adjusted and getting many C's in a roll), so I started out having 2.3 overall. When I was about to graduate, I pulled my GPA up close to 3.0 with an Honors Thesis, and got accepted to a top-20 PhD program in my field (of course, not without my supportive LORs). There is hope.. It may look tough, but don't loose hope!
Is there a reason that you are only interested in the very top programs? If your main goal is to do research in your field, and location of the school is not that important for you, I read somewhere on this forum that you can look into schools in the Midwest or South region. There are also good research institutions at these places, and less competitive (my guess is coast regions are considered more habitable to most people..). This way your chance of being admitted to a program would increase.
Just my 2 cents based on personal experience from this current application season. Good luck to you and you will be fine!