After all of that... BA sent me a note saying oh sorry, we didn't actually cancel your flight, carry on...
So now it's back on schedule, and assuming no delays 3.5 hours is sufficient time to get transferred from T5 to T3. If there is a delay on BA's part that causes me to miss the 137, I'm probably toast because now the remaining VS flights that day are all going to be full up, but then I get to spend an extra couple of days in London with perhaps some EU261 compensation to cover some hotel expenses.