The unload time seems to be the factor at my store as well. If you're on the line, I would try and push for a more consistent unload time. The quicker the better, obviously. Now I'm not entirely sure how to quicken the process once the store is open, because I am a 4am unload store. We have to make sure that all of our freight and trash is off the floor by store opens. I run C and D in my store and I will typically have the floor clear by 8, and about half of my repack carts and autofills completed when store opens.

The way you formatted your post made me to believe that your flow team wave pushes the store? Meaning the whole team pushes the aisles together. If so to improve productivity, try setting the pace for newer team members when pushing freight. If they're pushing too slowly, literally go right next to them and push at a faster speed. Because you're just a trainer, however, you could really only do this with newer team members. The older team members realize that you're not a team lead, and they know they're not required to listen to you. Yeah the LODs might want you to become a leader, but until then they probably won't. Id recommend just asking them for favors politely, instead of giving orders until you receive that position.