Gee that sounds like my story.
After much consideration and even booking into hospital I am going the homebirth option.
You could have intermittent monitoring with the handheld thingo, I think it is called a doppler. And yes I also believe being able to move freely will help the baby move down and avoid being distressed.
When you find an ob you will probably have to negotiate on what sort of monitoring you want, at the end of the day is up to you of course, but I personally didn't want to have to deal with getting to hospital to have them tell me what I should be doing, and risk failure to progress due to stress.

Have you organised to get your hospital records at all?? I did and it was an eyeopener, my supposedly distressed baby who was 'stuck',(at the time that is what they said), really had 'descended well' and had a heart rate that didn't go below 120 (according to the notes). Hmmm...