Adding distance/time into your program is probably going to help, as long as you don't feel too tired/sore or that you're over-training
Consider adding interval training to your regime. That's a more time efficient way of improving your VO2MAX (which should translate to your overall performance). E.g. 1-2 minutes 90%-100%, 1-2 minutes walk/slow/jog, x3-5 (this is rough, do some reading and see what works for you).
When biking, it really doesn't help that I have some silly hills surrounding the house. Even if I'm not going all out, a 10% climb takes its toll.
Now that you've recognized how gentle a low heartrate feels I'm sure a conversational pace is totally adequate for staying under your lactic threshold (but if you could sing you're going too slow!)
For a beginner a good tip is just to go a little bit easier than they think they should be going. Once you've built some sort of aerobic base your training should start including intervals and runs that push you harder.
There are two risks in pushing yourself too hard. Injury and over-training.
EDIT: another thing I didn't mention is that in terms of injury you want to give your body plenty of time to build more distance. Most of your joints and other tissues take longer to adapt than cardiovascular. I think this is where people can get into potential injury situations by ramping up too fast. I personally also try to run on soft surfaces (trails etc.) since I find hard surfaces (roads) a lot more punishing.
I pretty much settled on what all they were saying. I was taking the exact path you outlined. Since that seems to be working fine for me, and I'm also adding weights, I figured I would wait and try again later. Probably in a year or so, if I can keep up this schedule. Good luck on your exercise!
My heart rate goes down way faster, so if I stop for 1 second (literally), my heart rate drops immediately and it takes a lot of effort for it to go back up.
I suspect at this point training in zone 2 is trivial, my body gets naturally there
TL; DR; train hard first, your heart gets stronger and brings you to zone 2 naturally?
I'm no athlete or expert, so please do your research and ignore everything I said