Caitni I ABSOLUTELY feel your pain. I have been in your position twice and I would love to be able to say that this one came naturally.
You do right to be trying everything you can to get baby out and everything you're doing sounds bang on the mark. Remember that what you want is as much "head bumping against cervix" action as you can get. Bounce on the birthing ball, walk up and down stairs. Get down hands and knees if it's not to painful to make sure the right bit of baby's head is touching cervix.
If you're booked for the induction on Tues, my advice would be to try to be at home on the Monday night ( unless you love hospitals and would rather be there). I slept little enough as it was the nights before my 2 inductions and was very grateful of the chance to be in my own bed.
To reassure you - if your cervix is at 2/3cm , effacing and moving forwards on its own you will probably be getting very close to being in labour anyway. Chances are your waters will go soon if you're at 3cm esp if you're moving about. And if if IF you do end up having to be induced it will almost certainly be a very quick experience if you're so far along already. Prostin , a quick walk and a birthing pool in hospital. (that was exactly my experience with DC2).
I KNOW you don't want to be induced. I don't either. Stupidly in my heart of hearts I feel like less of a woman for not being able to go into labour naturally. PLEASE DON'T feel anything like that. No one is judging you and what you do for the next 18 odd years AFTER the one day of giving birth is SO much more important.
Pleas repeat all of this back to me on April 9th when I'm in the same boat.