That outlook actually helped me solve some of these.

Once I respecified the problem as "accept .*BB$" it became a lot easier to visualize. In particular, it showed me that I needed a junction at the end which passes only an empty tape. You can, in fact, code it up by creating a piece that accepts anything (except end of tape!), two pieces that accept blue, followed by one that accepts only the end of tape and wiring them together properly (which I leave as an exercise for the reader; I'd hate to spoil any of the problems too much).