Thank you for your question!
This is a very common thing that most of us can identify with.
It definitely takes time and lots of practice to be able to hear what you want to play, like Joe said. But it's definitely not impossible to achieve.
Overthinking is something that most of us do from time to time, and I think the more I've practiced soloing over common progression the less I have to think when I play. I try to simplify things as well, for instance, the ii V I progression that happens in (almost) all jazz standards as well as in the Jazz Blues. I often times don't think too much about the ii chord. (Dm7 in your example). Joe Pass said once that he completely disregard the ii chord in a ii V I progression in the blues. He's thinking V I.. that ii chord is just "something that comes with it"... a suspended V chord, in a way. So you could use all the "tools" shown in the "Jazz Blues" lesson, and start playing the diminished (for instance) already when the ii chord comes up.. cause it goes by so quick and we actually just hear that V chord being altered in some way, we don't think about the clashes that may happen when playing altered scale over the ii V or even the diminished scale.
But that was just a side note.
The difficult part can be to learn to resolve the line on the next chord. It's important to land on a good note and I think this is very good to practice. That's when we hear the changes, when resolved in a good way. If you add some practice time where you only focus on playing simple ideas that resolve in the right place. Maybe play a line and resolve on the 3rd of the chord, 5th of the chord or somthing.. that helps a lot for me. So maybe play a simple line over G7 (like an ascending G7(b9) arpeggio starting on the note B, (major third) over the G7 chord and then resolving on the major third of the C chord.. for instance note choice could be: B, D, F, Ab then down a half step to G, then F, and then D, D# to E, in a chromatic way to resolve on that E.. Difficult to explain in text, but Maybe you can try a simple lick like that and really really nail the resolution and use it in different places in the jazz blues when playing on a chord that leads a 5th up like G7 --> C or E7 --> Am.. (but then resolve on the minor third of the A chord obviously)
You'll be able to hear more of the lines the more you practice and get comfortable with the changes.
Hope this helps a little and let me know if you have more questions! The "JAZZ LINES" (vol 1) lesson about the ii V I can be a good video to watch for you I think!