I have been able to on occasion find two J seats on YQR-YYZ-LHR runs with AE (sometimes going through YUL as well), but I think the AE website is a poor tool for finding those seats. I use KVS Tool, which searches via the ANA Tool (you can access the ANA tool directly off the ANA website and by joining their FF program) to find availability. I believe that Expertflyer allows similar searches. When I have booked AE rewards, I have always used KVS as it allows me to see exactly what is available and if the website won't show me what I know is available, then I call in to make a booking.

I believe that award availability is dynamic--e.g., seats can open up over time--and that the number of seats available on any given flight is variable, so it can be zero on one flight and then it could be more than one or two.