Personally, I’d avoid the LHR/LGW transfer hassle and try to stick with a flight that gets into LGW to begin with if going to MLE.

Here are things to consider to truly maximize your awards to MLE:

• Per AA All-Partner award rules, one is allowed a free stopover in North America gateway on an all-partner award flight in each direction (See "All Partner awards" -> "International Free Awards")
  
• North America also includes the Caribbean
  
• You’re not allowed to claim awards on BA flights between the US and the UK, but you’re definitely allowed to do so between Canada, Mexico, and the Caribbean and the UK.
  
• BA flies lots of destinations to/from the Caribbean to/from LGW

With that knowledge in hand, see if you can insert a freebie stopover at a Caribbean destination on your way to/from MLE. Visiting three island tropical paradises (one on the Caribbean on the inbound, MLE, another Caribbean on the return) is better than one, moreso when it’s the same amount of miles. Plus you avoid the hassle of transferring between LHR and LGW

So the routing in the case would be something like LAX-(connect @ MIA or SJU)-(Caribbean freebie stopover A)-LGW-MLE-LGW-(Caribbean freebie stopover B)-(connect @ MIA or SJU)-LAX (red denotes AA flights, blue as BA flights)

Alternatively, North America also includes Mexico and AA partner Mexicana flies MEX-LGW so that’s another option you can opt for in one of the directions. Go see the ancient Aztec ruins of Teotihuacan to start off a trip to MLE