BB engines are offset to the passenger side a little bit. The BB motor stands are different and would push the engine to the passenger side. Crossmembers are different, shifter mounting bracket and linkage are also different so the stick still ends up in the same place in the console.
You can continue to use the small block parts and fight the differences as is now OR go find the big block parts: crossmember, motor stands, mounts, bellcrank, shifter bracket, linkage etc. and swap them all out.
The starter, clutch, flywheel and bellhousing all need to have the same application in order to fit and work right but they can all be from any one application SB or BB. You can not mix and match these items.