You said your HR was constant while doing the step-only premix (no interval blasts). So, I would expect your HR to remain constant during this workout. I see no issues here.
Also, your max HR does affect your HR during exercise - if your MHR is high, your heart rate will be higher during aerobic training than it would be for someone with a lower MHR.
It is true that recovery rate is a good indicator of cardiovascular health. A 15bpm decrease during 1 minute of cooldown is a good recovery rate. Check this during your workouts.
If signal interference was to blame for the HRM readings, it would most likely appear as random spikes in the HR data, rather than consistently high or consistently low. Checking the battery on your HRM might not be a bad idea, but if you have had high results like this since you first got the HRM, I would not suspect the HRM, unless it's a manufacturing defect with the HRM. Try taking your pulse with your finger and compare it to your HRM reading - are they close?
I have used 208 - (0.7xage), but it is still not close to my actual MHR. Actually, it gives me a lower MHR than 220-age. None of the formulas are remotely accurate for me, even the gender-specific ones. The only way to know your MHR with any certainty is to take a stress test.