For an hour of exercise, being in the "fat burning zone" means you burn fewer calories. But as you have discovered you can do more of it. So you can burn more total calories than if you go all out, although it takes more time to do it.

Rather than plan the optimal training for losing weight, I suggest picking an athletic goal. Like completing a metric century, or a 10k run, or whatever appeals to you. Working towards that is a more interesting and motivating goal than "weight loss" but will get you the additional exercise to enable the weight loss. And it's way better than trying to "beat" yourself on every ride. You become a better cyclist through both training stress and rest. If you only do one you won't get far.

Running every day for an hour is tough on the body. Unless you have been doing it for years its likely to result in injury. Even when I was a hard core 20-something runner I didn't run more than 5 days a week. But I'm 30 years older now and I can handle 12-17 hour weeks on the bike with no problem.

On week off every two months is probably not enough. Depending on my training load I do an easy week (not a full week off) every 2-4 weeks.