Once I was in very active labor, I did not want to walk around or even move more than gentle swaying. Mostly, I wanted perfect stillness so I could turn inward, but that's how I dealt with the pain. It may be different for you.
Continuous monitoring doesn't have to ruin your birthing experience. The way it is most likely to have an impact will be keeping you away from the birthing tub or shower. If you have made it clear that you want to be able to change positions and have a natural birth, your hospital is likely to assign you a nurse who can help you do that even while being monitored. I had one continuously monitored labor, due to induction, but the nurse really helped me change positions, move around some, and worked with me even while being monitored, and I wasn't being monitored by telemetry. If your nurse cares more about the monitor than you, then you can have your husband/doula/other support person ask for a new nurse.
Does your doctor prefer continuous monitoring, or does she require it? Can you get an agreement on an intermittent schedule? I don't think you can assume she's a knife-happy physician just based on this, but it may be worth reconsidering your choice of care provider.
Transition is sometimes considered a subphase of "active labor," and in these cases "active labor" is used to refer to the time from about 4 cms, with strong regular contractions, until full dilation.