Walking over seedlings TTTF/KBG and overseed timing

Hi All... we have seeded an 80/20 TTTF/KBG lawn in a mixed sun/shade area (couple big trees). Originally had everything down 2 weeks ago with wheat straw, then did a little with a little bit of reseeding after two days of crazy heavy rain. Sunny areas are about 1.5 now and the shady areas starting to pop. Now today more heavy rain.

I know I have to reseed AGAIN where straw got clumped because I can see where it's not coming up. Want to address it by loosening up the straw in a tactical...

Walking over seedlings TTTF/KBG and overseed timing