(((hugs))), don't feel bad about the monitor, it's not your fault and I'm sure if/when he woke it probably wasn't for very long. My guess is that if he saw you not by his side his fussing was short lived and he fell asleep quickly. Just look what happened when you left to wash your hands- it sounds like he would have been up longer had you of been in the room. Please don't blame yourself and don't be upset, this was out of your control, you didn't let him CIO, letting him CIO is making a decision to let him cry and not go, you did NOT make this decision, you had ZERO control as you did not and could not know the monitor wasn't working.
First, I don't think I'd do anything until this round of teething is done. You've AP'd until now, a little longer will not hurt, at least until he is not bothered by current teething so that he can also focus better. He will feel like he needs you more now if he has pain from the teeth. Also, is he on meds for his reflux? Does he need to be? I would want to get this under control too, before you start sleep training.
When you do start, I think I would first want to try to get him to love his bed so he doesn't fight it as soon as he's put in. Maybe put him in there with some toys while you're in his room dusting or putting away laundry, just a few minutes at a time. Maybe somehow try to make it fun even. Try reading some books to him in there too. Anything to get him comfortable with the crib again. Maybe even buying him a new "special sleep friend". When my dd was young we got her an angel doll that we hung from the corner ceiling and it was her "sleep fairy".
To stop the rocking, I think I would start with a combo of PU/PD and gradual removal. So, if/when he starts to freak, pick him up, stroke his back until he stops fussing, put him down. He might be heavy or big for the constant PU/PD that might be needed but since you've been rocking and he's had that close contact then he might need you picking him up, stroking his back to say "it's ok". Then tell him "mama's going to be right here" and sit in a chair beside his bed. Then, nightly, gradually move the chair until you're outside the door. I had to do this with my dd when she had hit SA, it didn't take long, my office is just outside her room so I remember even sitting at my desk working and having to leave her door open and she'd call out and I'd say "yes honey, I'm right here".
So that's what I'd do, hopefully you will get some more ideas and help from the lovely ladies here. I just couldn't read your post and not reply because I really felt bad for you that you felt bad for something out of your hands that you had no control over. Again, (((hugs))).