A new TL taking over a failing workcenter is never fun and presents its own challenges. The bottom line is that you are in charge, meeting resistance is unacceptable and it's something you need to nip in the bud. If things were not working before you were a TL, who is the problem? The TMs.
By not having to push market or SL, you save around 4-5 TMs, so if you have 12-13, a regular flow team would have 16-17. 16-17 TMs scheduled 4 hours (64-68 hours) for average sized 2000 piece trucks just isn't enough, not even close.
But from what you have said you are doing and with the TMs you have:
2 people throwing to 3-4 people doesn't work. 1 person can throw to 3-4 people or 2 people can throw to 7-8 people. With 1 person, you want a rate of 17 boxes/minute and getting 2000 pieces thrown in 2 hours, and with 2 throwers you want 34 boxes/minute that will throw 2000+ pieces in an hour.
When does SL need to start getting pushed? If no one is pushing it until 8:00 or after, then I would take all 4 hours to break it out having just 1 TM do that.
Bowling HBA into carts really doesn't make a difference from bowling that section on the floor. Just make sure whoever is pushing the cart keeps it at their hip and isn't walking back and forth to the cart.
Since every store is different, no one knows what C/D is at your store, but, I'll just assume it's housewares. If that's the case, why aren't you bowling Toys, Sporting Goods and Seasonal?
If you are really doing push all with that much freight coming weekly (one of many reasons showing your STL has no idea how Logistics needs to be done), then I would suggest replacing a section of pallets on your line with flats. HB01, HB02, and PHAR fit nicely on flats and make bowling the front of the store much easier. Since 4 flats fit in a section, I'd add PETS or non-laundry detergent CHEM to a flat as well.