The ledger board or stringer you mentioned is crucial for support. Especially with the weight of cast iron. If your having trouble with a horizontal stringer, then simply measure and cut vertical 2x4 supports. Three of them is adequate, one at each end and 1 in the middle. You can also "mud" the tub in. I do this on all my whirlpool installations to minimize shifting, and for soundproofing. You simply mix cement dry (60 lb. sakrete or sand mix) and set the tub in the mix. Keep the cement away from copper lines. Good luck Karl with the new tub!