Martha Eleanor is a gorgeous name!
Assorted thoughts: I’d probably go Marty/ Martie or Marnie (with the N from Eleanor), or maybe something very posh and fun like Moppy which means Martha would also get used. Mimi wound be cute - the Me-me version.
I like Emmy and Hattie too but possibly too far from Martha - I’d want to keep an M name, I think. Hattie is very cute though! Polly is another option in that vein (and I prefer Polly to Molly).
I’m not a massive Mae fan myself but the MaE spelling definitely works. Matty is a little too 80s boyish for me…