Cross training won't hurt and it's recommended for runners to reduce the risk of overuse injuries while building aerobic capacity. But if your goal is to improve at distance running then you're going to have to run.

Instead of grinding out a slow 11 minute mile try running at a 9 minute pace for a shorter distance. Then rest for a few minutes and repeat several times. Do that a few times per week and gradually increase the distance you run at the 9 minute per mile pace. Eventually you'll get to a full mile at your target pace.

Also if you're overweight you're going to struggle with running and be at higher risk of injury. If that's your situation then stick to lower impact sports until you drop the extra weight, then ramp up the running.

I was underweight and borderline anemic through early 20's and it didn't make a difference, but still huffed and puffed. I could do low intensity things like cycling for 10 hours a day, no problem, but jogging, swimming, or running would make my descending aorta vibrate my lower abdomen and maintain a typical hr around 120-140 bpm (resting bp was 100/50, now resting hr is 115 with bp 125/80). Trying to discontinue propranolol for endogenous? tachycardia with hypertension.

I'm in the process of losing 40 lbs (17%, cut) and then rebuilding muscle mass.

There is something wrong with your cardiovascular system. Have you been screened for an abdominal aortic aneurysm, patent foramen ovals, or arteriovenous fistula? A resting heart rate of 115 is crazy high. Get a second opinion from another cardiologist. Ask for imaging studies, treadmill stress test, and a Holter monitor. Good luck.