Running with a heart rate monitor can be very, very frustrating. Been there. And yes, you will take quite a few walking breaks for a while!

A couple of things to consider. I was a runner before I was a cyclist. I cannot get my heart rate up as high on the bike for the same "level of effort" as I was when I was running and in very good shape (better than I am now). In other words, cycling seems to be easier on my cardiovascular system. Maybe something like that is happening to you (and maybe not...maybe I'm just a weirdo). Also, you didn't say how you determined your max heart rate and your effort levels, but make sure you really know what your max is before you start doing the rest of the math. And there are many different ways to "do the math"...I always used

target heart rate = [target percent (max-resting)] + resting

Example for 85% effort level target rate =[85(max-resting)] + resting

Where resting is your heart rate laying in bed in the morning, before you do much other than move your fingers & toes. This was from a running coach that I used for a very short period of time. I haven't tried it cycling.

If you want to know how to do a really simple max heart rate test, PM me.

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