SJU is on the list, so LAX-SJU is considered a transcon. The longest is actually LAX-SXM, though there is no return flight and it is in biz. Well, for that matter, so is SJU.

Yeh, if you transit LAX, then you are fine.

You can hop inside Africa on the BA affiliates. Comair, for example.

If you are in JNB, you will get out or in via HKG, LON, or SYD.

As far as the in and out of Europe thing, BA has done something stupid. This isn't an opinion, this is a fact. They have removed MRU, NBO, and SEZ from the list of places that you can re-transit through London to get to or from. Basically, they have effectively removed them from possible places that you can visit, if a tariffs robot goes strictly by the rules. I think you should be able to talk to them and get them to accept logical thinking, though it is not a certainty at this point.