I stumbled on a work-around fix, sort of. I highlighted the video clip, cut it -- causing the transitions to be eliminated, and then pasted the clip back in. I thought maybe once those particular transitions went away, the rest of the transitions in the project would somehow be freed up, but no luck. Even a new transition is locked in place. Weird...
Hope there's a solution... not being able to eliminate transitions without cutting and pasting the clip eliminates a lot of flexibility.
And I'd really like to solve the other issue, too -- where a piece of audio repeats during the transition. Again, I can mask it by sliding something else underneath, but it shouldn't be happening at all.
Appreciate your input.