[potamic]

That's what I do, zone 2 training. I use a chest strap monitor too. 30-45 min sessions, 2-3 days a week for months altogether, mixing it up with intervals some times. I've done this many times over in my life, never seeing any improvement. Even today, the smallest of jogs will take me to max HR within 10-15 min.

[xarope]

Do you have any medical conditions?

Assuming you've had yourself checked up, and do not have any medical conditions, then maybe you are just aerobically deficient (https://uphillathlete.com/aerobic-training/aerobic-deficienc...). Start slower, doesn't matter if you are walking. In fact, if you are doing 3x45 mins of zone 2 each week, start doing 2x45mins of brisk walking to keep your heart rate at zone 2. After about 4-6 weeks, you should find that you can start jogging again and hopefully (!) your heart rate doesn't peak so fast.

(I'm assuming a lot of things here, namely that you know what your LT1/LT2 are so that you can accurately calculate your 5 zones; https://www.trainingpeaks.com/learn/articles/joe-friel-s-qui...)

[vasco]

Is there any reason for such strictness with your heart rate? I never measured anything and always progress up to a nice speed, and then it's when it flattens. Mix up the trainings and leave the HR monitor at home. Do ones where you just sprint as often as you can and others where you go slow, if you see some stairs during your run just sprint over them, etc. Of course, only if you're a regular person without existing heart issues.