Andrew I've been going through the same exact thing lately (well before I tore the tendon in my shoulder), and I'll be honest, I think I did it wrong.
I thought that getting in longer duration medium intensity cardio was the best way to build up endurance, both muslce and cardio vascular, and it is you will need that and yes it helped me lose some fat too, but personally I find Hiit to be so much more effective at fatloss, that i now feel like I should have done 4 to 5 weeks of hiit for fatloss, then started supplimenting in the longer duration runs.
The reason being, the long duration endurance training will be much easier to do the less fat you have on you. Just my .02
I don't do this for my family, my friends, women, accolades, pride, or ego. I do it for me and no one else, its just part of who I am.