That's great, Mad Rook, thanks again. I saw Heisman's book at the library and checked it out (literally and figuratively) and decided, first, that the book was in its own niche if not unique: a book explaining how to think about chess (i.e., structured thinking processes) as opposed to a book on tactics, or strategy, or openings, or game collections, and so forth.
Second, I decided that Heisman had hit the bullseye when he said that the failure of the average class player (especially those rated 1800 or under) to rise to the heights (even if only the middling ones) is due to their tendency to play "Hope Chess" or even "Coin-Flip Chess" -- that is, failing to check basics such "if I make this move, what are ALL of the checks, captures, and threats my opponent can make in reply, and can I safely meet them all?" and similar considerations.
If players aren't applying themselves to the basics each and every move, then everything else they do to improve their chess is built on a foundation of straw. So, I decided that I would distill his book suggestions into something I could use personally, and use correpondence chess as a venue to learn how to apply them and get in the habit of doing so. I still haven't come up to Heisman's standards for "real chess" (not systematic enough, I fear) but I've made a LOT more progress in my chess since I ditched the databases and started thinking from first principles, with an eye to the concrete situation at hand in each position.
True, I take a lot of time playing chess this way, but there is no way to develop the skill of "reading a chessboard" accurately, selecting good candidate moves, and finding the best one among them, except developing those skills by practice; and real games are the best way. Using each move as a kind of "exercise" also gives plenty of opportunity (and motivation, since you're actually playing) to develop tactical skills and strategic judgment. I figure that the more I develop and use such skills, the faster their application will be as they become second nature and as I gain experience with them; so for me the formula is "develop the skills and the speed will come with practice and use".
Edit addition: Another advantage is that analysis is a skill which requires both concentration and mental stamina, and the latter must also be developed, so I find myself able to "take on more" over time as I practice some of Heisman's techniques.