It is not that odd to find that you have a confirmed reservation but there are no pre-allocatable seats. Some unallocated seats may be blocked, and BA may already have accepted more reservations than there are physical seats on the aircraft = overbooked, as is very common. It sounds like you're travelling at a high demand period. And, as you say, it makes sense that you can't pre-allocate a seat on a flight on which you have no reservation but simply a waitlist request.

I don't have personal experience of BA's waitlist process, but from what I hear about others' experiences, don't expect it to be particularly scientific. You may want to set an availability alert on ExpertFlyer so that you can call BA yourself (or call your TA) as soon as you know that a seat has become available on the flight that you want but the waitlist process doesn't clear your waitlist request immediately.