Ok update time. I removed the rod holding the back door in, and I removed the back door, then I removed the springs.
Turns out, the springs are both in perfect condition!
The problem seems to be that the door has a little hole in its plastic that the springs slide in to. And that hole has significantly elongated, to the point where the springs aren't really pushing the flap down until its opened quite a bit. I'll try to includes some pictures below.
Those doors are quite pricey, $50+ for a new one. So I don't think I'll replace it. If theres a way I can fix those holes so the springs sit properly and put more pressure on it, thats great. Otherwise I might just leave it as-is. Any thoughts on how I might be able to fix this? I can't think of anything that wouldn't be very temporary. Like smearing some JB Weld into half of the holes, or trying to cut a washer with the right, smaller hole, and then using something to 'glue' that to the flap itself. Maybe some 3M 5200 would work if I really cleaned the plastic first and also scored the washer glue surface a lot. But this will be a real pain in the ass, I don't want to do this.
I just had a thought. Even though it's the flap side of the spring that's having the problems, I could still potentially fix it on the other side. if I could do either of these things reliably, that could fix the problem: Put some kind of spacer between the spring and the mower body that would push that end of the spring out, thereby pre-tensioning it. OR snipping the end of that spring off entirely, and re-bending a new "L" into the end of the spring, that would be further along the coil. I'm not sure how easily either of those ideas will be, I'll have to take a first hand look tomorrow with those in mind.