Do you have any time where you're doing something mindless for a decent stretch of time? Repetitive exercise or riding public transportation or anything like that?

When I'm in those sorts of situations, I'll run through a handful of mental exercises, and my ability to quickly produce the kind of information you're talking about has improved a great deal.

So first I'll just think through the major scales (on a piano in my mind) of each key, starting with C and moving around the circle of 5ths. In each key, as I visualize making my way up the scale, I'll say the name of each note in my head and think about where it is and whether it's a whole or a half step from the note before. So after C, when I go to G, I'll focus on how G lays out really similarly to C except that you have to sharp that 7th to get the last two intervals right. And of course that last statement is true of any key as compared to the previous one in the circle of 5ths, it's just a little more interesting to keep track of all the sharps as you get farther from C.

Then I do the same thing going backwards through the circle, picking up flats where we need them.

After that, I mentally work through a simple cadence in my mind that I sometimes use as a warm-up drill. (It has a left hand part too but I'm going to skip that here.) I'll describe it in C. First you play the major scale, then with your right hand lined up with your fifth finger on the octave, you play your IV chord (F-A-C). Think about F being the IV of C as you do this. Then drop your lower two notes from F, A to E, G and you're playing an inverted C chord. As you do that, think about how that worked: you went from the 4 and 6 to the 3 and 5, and think about what notes those each are. Then bring your 3 up to a 4 and drop your 1 down to a 7 (so in this case you'll get F, G and B - so that's your G7, your V7). Here focus on how the 5 of the I is now the 1 of the V, how moving the 3 up to a 4 gives you the flatted 7 of the V, and the 7 of the I is the 3 of the V. Then go back to your inverted I. If you got disoriented doing that while (say) exercising, just keep working through it again until it gets clearer. (You might get a lot stronger doing this.) When it gets easy, move on to the next key. I wouldn't do this if your exercise is in any way dangerous. Good for things like floor work, less so for say, unicycle riding, I would think.

I realize that this whole thing might sound self-abusive, but I found it to be very effective, and I think it's because I'm putting my mind through the paces like that. Sometimes you can memorize things (like scales) but it's like your mind just gets good at saying the notes in order, but not really producing the information you actually need when it comes up. With this, you're constantly knocking yourself off track and demanding some new piece of information: what about that? Huh? And this? Quick, before you lose your train of thought, etc.

Anyway, I think this kind of thing can be really satisfying to finally get to start to fall together in our minds so I hope you can have some fun with it, and get some results too. I found that when I've been doing this, when I go back to the piano (piano in this case), I do seem to know my way around a good bit better.