After some encouragement from other people here (thanks again guys, if you're reading this xx), I put aside my doubts and attempted week 4 for a second time, instead of repeating week 3 (again) as I'd planned.
It was....really easy. Sure, I was soaked in sweat and pretty exhausted at the end, and yeah, my legs started aching (a first!) about 3/4 of the way in, but I never reached anywhere near the point where I couldn't physically go on, which for me is all I'm hoping for at this point. Considering last time I tried I hadn't been able to do a single one of the runs without cutting it short and starting late, this is a huge improvement for me, and I'm frankly ecstatic that I have genuine proof of my improvement.
I do really need to get my playlist sorted, though. Every time I get told to prepare for the next run I have to scramble to get a good song going to get me in the mood - half the time I'm frantically shuffling things on my IPod when I should be focusing on the running. One thing I really liked about the podcast before I switched to the app was that it took care of the music for me, and it was always a good beat.