So I've finally figured out the issues with the slow downs. I tested the old theme on 10 year old systems, and never had any performance issues with it, but they were all desktop computers with at least decent graphics cards. I'm noticing that on my laptop, which is 4K but does not have all that great of a video card, it's way more clunky than I've ever seen before. So it's obviously graphics-card or video memory related.
Furthermore, I've determined that the shadows on the boxes and the background blurring are causing the slowdowns. I'm a bit in disbelief that WPF would be optimized so poorly, especially with static blurred backgrounds, so my apologies that I didn't realize this sooner.
For now, I'm going to update the New Default Performance theme to disable the blurred backgrounds as well, which should bring the theme mostly up to the performance of the old default theme. Ultimately though, I'd like to improve the performance without resorting to removing those features, so I'm going to see if I can't make it happen another way.