MAF training while running has produced great results for me. I've made very steady progress and gotten faster.

Like you, the RPE while cycling made it hard to tolerate. Once I got a power meter I found that my MAF range correlated spot on with sweet spot based off my estimated FTP.

Since then I just ditched the HRM and focused on intervals with Trainer Road. Again, I'm making huge progress in power gains but I just don't watch the HR anymore. In my opinion it's not as critical for injury prevention like in running so I didn't want to feel like it was holding my back on the bike.

 
I would like to ask the forum members if anyone knows if there is a known relationship between MAF HR and FTP /Critical Power.

It will depend on how you arrived at your MAF HR. The 180 and 220 - age formulas are pretty random. MAF HR is roughly lower Friel Zone 2 or about 85% of LTHR. Friel LTHR is often determined by a 30 min TT with the last 20 minutes HR average being LTHR. CP30 is pretty much equivalent to LTHR.

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Are you using your run LTHR on the bike ?

I don't do MAF, but you need to do a LTHR test for bike and run if you want to do MAF for both. You will find your threshold heart rate running and cycling will be pretty different.

I just used the 180 formula. I read a bunch of articles, but i didn't see anywhere where he distinguish HR guidance by sport.

I do recall reading that he backed into the 180 rule based on a bunch of data points from runners specifically. The articles went on to apply the methodology to all endurance sports. I guess the methodology could be valid with different starting points for the calculation. Is there cycling specific guidance? Say a 160 rule?

I have used training zones before that were set by a Friel-like threshold test.

Is MAF equivalent to 85% of LTHR in each sport? If so then I can work with that. I would imagine RPE would pretty closely align between running and cycling.

I'm not sure, I didn't really know MAF was a thing for cycling, I'd die doing it at the same HR as running.

You maybe able to separate the heart rates if you measure an actual max for each sport and run the formula off that instead of guessed maxes. For example my max run HR was 202, where my max i could hit cycling was 187.

A better formula for experienced athletes is to train at LTHR-25-30 beats. This usually correlates with maximum aerobic pace.
My running LTHR is 10 beats higher than my cycling, so my Running MAF is around 145-150, whereas my cycling is 135-140.

The point is to train at your maximum aerobic pace, if you are exerting too much effort you are defeating the entire purpose of the workout.