LSMW is not really a tool for a standard business process, its purpose is data migration.
Picking/putaway strategies and data migration does not really fit together as well.
You are simply loading stock as is in the warehouse, a strategy might want to place it (or pick it) somewhere else. For this reason you usually use movement types that are customized to not create TRs and TOs automatically. Instead you would manually (or later with LSMW) create a TO where you define yourself from where goods are removed e.g. using movement type 999 to move the stock from the bins to the interim storage type in the issuing location and the other way around in the receiving location.
I would say create a new MM movement (copy of 311), setup new WM movement types and interface which does not create TRs and TOs automatically. Then it does not really matter if you start from IM or WM.