I'll start with an important note that I'm from astronomy and planetary science programs, which definitely treats the PGRE differently than traditional physics programs.
While there are indeed some schools that will filter you out simply due to your PGRE score, there are also some very good schools that will still consider and accept you even with a below-average PGRE score. I don't know how much money and time you have to apply to places, but since you are riskier, as admissionprof said, you might have to apply to more places than an applicant with a higher PGRE score.
I don't know how it works in Physics programs for sure. But people with 0th to 50th percentile PGRE score are regularly accepted into astro/planetary PhD programs that require or strongly recommends the PGRE.
I think the concerns regarding your foundational physics course preparation are valid ones. Personally, I see your research record and experience and I feel that should trump these concerns. Especially if you can address them via a multi-pronged approach: 1) get LORs showing that you really know your Physics stuff, 2) high GPA in upper level physics and math courses, and 3) improve your PGRE this fall as much as you can.
If you were applying to Astro or Planetary programs, I would say your profile makes you competitive for schools of any ranking, especially if you have letters or other support in your application to demonstrate your ability to take/pass graduate level physics classes at the school. Physics programs are more strict with your PGRE scores, so I would offer this advice instead:
1. When considering where you want to go, don't worry about ranking or competitiveness first. Make the first "cut" based on research interests and fit only.
2. For schools in the top 50 (I chose this cutoff based on admissionprof's advice to you above), contact people there. Talk to the profs you are interested in and tell them about yourself. Mention that you are indeed worried about your PGRE score holding you back and get their honest feedback on whether their department will really care about the score or not. This will help you determine whether it's worth it to apply anyways. You could probably do this AFTER your PGRE retake and new score.
I don't want to give false hope or have you waste time or money. However, I think it would be a shame to skip applying to really good fit programs at top places just because of one factor in your application. If it were me, it would be worth the 15 minutes it would take to correspond with each prospective advisor at places you'd really like to attend to just double check that your score may still be acceptable. I also have a different approach to applying: you said that you wouldn't want to get mostly rejections, however, I think that if you didn't get more rejections than acceptances then you might have aimed too low. You only need one acceptance, so having more than say, 2 or 3 acceptances (so that you have some choice) isn't very helpful! I would rather get 3/12 successes than 10/12.