"Within the 1960's model lineup, the A906, A806, A606, A206 (and maybe the A406 and A106) are the Motors, Pumps ,Transmissions and cabinets(forgetting about bleach dispensers) interchangeable?"
Motors interchangeable from 1956-2006 helical (I think a few AMPs snuck into the early years).
Pumps interchangeable from 1956-2006 (minus AMP).
Transmissions interchange: First generation 1956-1965. Second generation 1966-2006.
Cabinets:
1956-1965: I never tried mix-matching 1950's cabinet parts with early to mid 60's parts or vice versa. Some will work, others may not. The early 1956-1965 bases went through a few changes. Obviously the pivoting motor base is not compatible with the sliding motor carriage base design but later sliding motor carriage bases with bigger springs are backwards compatible with earlier versions.
1966-1979: Completely interchangeable. Most cabinet parts other than the top (console mounting) are compatible with later models. Base interchangeability from 1966-2006.
Small inner/outer tub 1956-1993 (may be some incompatibility with very early helical models as there were some funky AMP tubs used).
Large inner/outer tub 1966-1993.
Tub covers, triangular seal, and metal band clamp 1956-1993 (minus AMP).
Unsure if tub bracing is the same on the 1994-2006 models as the previous 1966-1993 models.
Unsure about console compatibility/mounting on 1994-2006 versions as previous 1980-1993.
1994-2006 has their own inner and outer tub/tub cover design. Also their own water valve, injector, and fill flume.