You have to run (for 20 minutes) with a chest strap, but it doesn't have to be any particular strap.
If you don't already run, it kind of sucks, and that's a bigger "cost" than the Garmin. Twenty minutes is a long time, running is high intensity, sometimes I feel like I'm going to die when I'm running. It's not something I'd take lightly. But if I was under doctor's orders not to even get into HR Zone 5 because I might die from it, I'd consider this. Desperate times call for desperate measures, and all that.
I know a lot of people basically assume your LTHR is 85 % of your maxHR and that seems to be what the doctor in this case is doing. Except we don't know jtaylor's maxHR, and the 220 formula isn't very accurate for this. I haven't used the Garmin thing and it may be just as bad; it's at least another option though.