My basic mental formula is just to first fix edges that are flipped awkwardly, then position red opposite orange somewhere on the cube, and blue opposite green, and then stick them down there 2 at a time (not necessarily in that order, but that's the gist).
When I put the edges to the bottom, I do it so that red is in front orange on the back, blue and green on the sides, regardless of what the centers are, then I just do a final D/D'/D2 turn to align the cross to the centers (which I'm now trying to change to a u/u2/u' turn because the D turn sometimes confuses me when the first F2L corner I'm looking at while forming the cross is at the D face).
Just by doing that, just while practicing CFOP normally in a week, I managed to unconsciously get my cross time to sub-3, with my moves almost always being below 8 (although even with the rare 9-10 move cross, it still doesn't go above 3 seconds, so I don't mind).
Some recommend memorizing how to form the cross, then doing it blindfolded/with your eyes closed. I personally never did this training, but it wasn't hard when I tried. Just develop some system or your own personal way of managing the edges, like that thing with pairing up opposite colors.