Tyler O. answered 8d
Flexible and creative music tutoring
Follow your heart! There's never going to be a way to "correctly" solo -- what you've been training throughout your music education isn't your ability to seek a correct answer, it's to trust in your opinion. You're already doing it -- "I find that when I try to improvise over more "non-standard" progressions (for example, a 1-flat7-4 progression like EMaj-DMaj-AMaj), I'm pretty much lost." You NOTE that you are lost. You see it! Ask this question of the jazz greats and they'll give you the same nebulous answer. Vibe and trust.
To quote coltrane: "I don’t know, it seems like it gets harder and harder to find something different on it. I’ve got several landmarks there that I know I’m going to get to so I try to play something in between there that’s different and keep hoping I hear something different on it. But it usually goes almost the same way every night, every time."
Basically, he tries over and over again until something fits, then tries playing the thing that fits over and over again until it can't fit any better.
Trust yourself!