Hi Math,
Ive got a 2017 gt but thankfully havent got the same issue. Yours sounds like your starter or cable to the starter is getting hot and wont take the charge / turn the engine.
Have you recently put a custom set of headers on ?
My early mustang had a set of headers and same as your symptom, would start the engine cold, but not when it was warmed up. Fix was to put a heat insulator blanket over the starter, has been good since.
Not sure if this helps you , but good luck in getting a fix.
Regards
Mark