Wow. So you're complaining about having to complete paper work (I have had a problem exactly once with getting a signature, so I had the doctor sign instead of the nurse. Patients that are unable to sign don't count. There is a procedure to handle those signatures) properly and you can't sit out in front of an ER after you get done? To be honest, it sounds like a pretty easy way to make a few extra bucks an hour. Considering that I've seen people have zero problem sitting around for "their 20 minutes" (the company I worked for official limit for time between arrival at the destination and going back in service was 20 minutes. So if they got done in 5 minutes, they'd just sit in the unit for 15 before calling back into service. I've never been complained to about it regardless of if I took 4 minutes or 3 hours) after a call while the rest of the units run calls, this really seems like a non-issue.
To be honest, I'd be willing to bet that any delays that were properly documented and informed to management would be overlooked if brought up tactfully.
As a pure aside, for the love of all that is good, holy, and smells of roses, please use your enter key. Paragraphs are not the enemy, but a wall of text is.