I am also hoping for a VBAC later this year. For the past 3 yrs I have done lots of reading about VBACs and while there is question about the necessity of CEFM, many VBAC-supportive hospitals and OBs still require it. However, they usually require it once the mom is a certain # of cms dilated...so in other words, not immediately upon admission (except for the usual 20-min strip at triage).
For my upcoming birth I was happy to find a hospital that had telemetry equipment. This equipment is wireless so I will be able to walk the halls and get in the shower/tubs while still being monitored. This has significantly relieved my concern about being able to move. (With my first my water broke at the start of labor, so the hospital had me bed bound and I believe this was the main reason we ended up with a cesarean birth.)
Unfortunately, even very VBAC-supportive hospitals do not offer telemetry, but you might want to see if you can find one nearby.
HOWEVER, with all that said, from the many birth stories I have read, you can still have a very positive VBAC birth with CEFM. First, do not make the mistake I made, when the nurse told me I could not get out of bed even to use the bathroom, I believed her instead of simply saying I accept the risk and I am going to the bathroom like a normal adult. The nurse had me try to pee in a bedpan, which I simply could not do...so my bladder got really full, and a full bladder slows labor. I should say that if the water has already broke, there is a small risk of chord prolapse if the baby's head is not already engaged. Chord prolapse is a serious, emergent complication. In my case, the head was fully engaged so there was no real risk of chord prolapse.
So assuming your wife gets up and goes to the restroom often to empty her bladder -- which helps with the laboring process! -- she should take her time and enjoy the time off the monitors. If she has you or a doula to help her in the restroom, then the nurse should not have to be there to rush her back to the monitors.
Most importantly, check out this inspiring photo gallery of VBAC women laboring on CEFM. As you will see, the mother does not have to be stuck in bed on her back:
Hope this helps! And congratulations again!