While I can count pretty fast, my memory is miserable (only for this). And I keep on recounting many times from start, just one or two moves later.
I believe the best method for counting would be to keep the count for each group in mind all the time and just adjust by the move played last, so you have (when you arrive in the endgame) always a count of the board without having to go through all the unaffected areas again. This doesn't call for much, just keeping track of at most 10-12 numbers simultaneously of which only one or two are changing per move, but keeping even ten numbers requires some technique (at least for me).
What do you say?
Is it possible (sure it is) and how?
Do you know anyone actually doing this?
How much would it help to do this?
My memory for this is also miserable. A standard mnemonic I've heard about is the (Roman) rooms system, and at first thought territories are a bit like rooms. It's not clear though whether board positions in themselves can be made to have the same association potential as rooms in a home. Perhaps not.
Ultimately it would be excellent to associate the count with the sight of the pattern on the board, or even the sight of the whole board itself. Pattern recognition, and all. Apparently, professionals have this ability.
As far as I understand there are two operations here, one is the roman rooms / memory palace / journey thing (pegging), e.g. imagine the board as a room in your house and put the encoded numbers in it, but you can't imagine numbers, so you have to encode them, but in a way you can keep them easily when changing (as they do regularly). The question I ask myself is, isn't this more complicated in the end than keeping track of the numbers. Well, I need to try.
Associating the count with the sight of the pattern on the board isn't mnemonic technique anymore. You don't count and don't need to when you know the solution on sight, what I look for is a way to keep a dozen numbers safely stored but being able to change them continuously while playing, not more.
My advice would be: play your next x games with only this purpose. Never mind winning or losing. Play an intuitive game with not too much tactical distractions and keep track of the count of each group.
After x games, you may have developed an ability which will stick around for the rest of your career.
Currently, I'm doing something similar: I have the single purpose to get into a playable endgame and apply all my concentration in there to play the best possible endgame.
Bill: How about using number mnemonics? For instance, a territory of 21 points might be remembered as two turtle doves and a partridge in a pear tree. ;) Actually, too many birds in that song for me to keep straight. Maybe two shoes (one, two, buckle my shoe, Goody Two Shoes) and a red numeral one (the Big Red One) or Nixon (Nixon's the One ;)) or the Ace of Spades. :)