Check the driveshaft and rear end. If the driveshaft is unbalanced it can cause a good bit of shake...if the rear end is starting to come apart, it can also cause nasty vibration.
My 03 used to have a NASTY shake between 30-35, but only there. I found out when swappping from the 7.5 stock rear end, to an 8.8, that my 7.5 diff was pretty much destroyed. No shakes after that swap.
Also I would check the trans and engine mounts for sanity.
What do you mean by wheel trim?
With regards to balancing, did they use crimp on weights, or stick ons? If its crimp on, they are not as accurate and don't get to all the weight increments, so that could still be an issue. Stick on would be the proper way. I had new rims/tires put on my 04 F150, and the dealer didn't think there was clearance for stick on weights, so they used crimp on, and it shook real bad at highway speeds. I went back and asked why if they balanced it, it shook. The tech that did the work said it balanced fine, etc. etc. but I involved the shop manager. He went for a ride along with me and agreed it was bad. We took off the crimp on weights, and put stickies on and re-balanced and that fixed the issues on that truck.
Since you have new items in most places, I would assume that the hubs, etc. are clean and free of debris, and that the wheels are mating flush to the hubs.
Sumitomos are not a great tire but should not be causing an issue, Nittos have semi-bad treadware but again shouldnt be the issue.
Also, how are your ball joints, and tie rods? Any issues there? I'm also not sure what you mean by powerstop calipers, I didn't know they made a replacement/upgrade caliper.
What year is your mustang again?
2003 Redfire & Black V6. Full suspension, 8.8 w/ 4.10s, tuned. 4.3L stroker + turbo capable of 550 hp soon
DD: 2015 SHO PP, 12.87 @107 1/4 mile (1.8 60') on 93 octane tune/CAI only. SAE corrected: 369.4/451.4 on E20, full Bolt On