You can get UC rewards to MCO but they are extremely limited in busy times such as school holidays. And remember the 747s only have 14 UC seats
LHR-JFK is a popular route but there is still a lot of availability due to multiple flights for example.
You also need to be flexible and look at perhaps LHR-MIA or LHR-ATL which are on planes with a larger UC cabin (30+ seats) so more chance of rewards. Or a route such as LHR-JFK-MCO. - though of course they are less convenient than a direct flight which I know is your preference but the key to reward flights is flexibility.
I'd even consider sending one 1 parent and 1 child on one one flight and t'others on the next - not ideal but one way of getting 4 of you in UC
There are 2 rules (just like fight club) on getting UC rewards
1. Be flexible
2. See rule 1