You soo remind me of my situation when she was that age - she WOULD not sleep in pushchair or car seat either...remember pushing for hours and also car seat along motorway - once we did a three hour journey and nothing! So I felt your pain.
She did start doing the pushchair thing but not until later on, and often when I don't want her to, tsk tsk.
Gosh, I have no idea how you do what you do with three kids, but just wanted to say - you're doing them proud. Well done, it must be hellish right now and you must be sooo tired. I was getting EW of 4.30 and 5am for a long time too.
It changes a lot, but she seemed to be teething forever and that didn't help matters.
Sometimes, you can only do what you can do with everything you have on your plate. I hope someone has some suggestions for you. Perhaps try the long AM, shorter PM as you were thinking - though without APOP, will be tricky to get the second nap in from experience...I had to APOP the second one always.
Better go, think heating is too high and keeping madam restless. x