It may be that UA somehow benefits from enhanced award availability, but it is fairly well documented that BA will never be able to obtain more than 2 tickets at a time. BA would appear to be the most frequently used partner for EI redemptions, so UA experiences are a bit thin on the ground.

It could, however, be that UA's ticketing falls over when it actually does try to obtain 3 or 4 tickets.

Should you ever in future again attempt to book 3 or more J tickets in the one go, please come back and report your experiences. But I think it likely that you may find that availability is actually restricted to just 2 seats as the UA tool is probably not designed to cope with the apparent EI discrepancy of not advertising the exact number of seats available to redeem, and therefore the "error" may not be uncovered by the UA tool until it actually does try to book those (possibly non-existent) third and additional seats.