"I would appreciate some examples from those of you that don't use CT at all on how you use the trim tools in a typical sortie."
FWIW I do not use 'speed' trim, just level and angle features. And the only time I use those are in non-combat environments such as when in level cruising, climbing out from takeoff or being low from a fight and grabbing altitude again or when in a shallow dive to landing at home.
I have a good CH setup: Pro throttle, F16 Fighterstick and Pro peds (thanks to Vermillions good advice 4 years <G> ). I placed my manual and auto trims on two 4-way thumb hats on the stick. I have my elevator and ailerons trim use one 4-way hat while the rudder trim uses half another along with the auto angle/level trim functions.
When I am level I take off auto trim and go manual. Note: I use different machinations depending on if the torque is CC or CCW. Because when you get slow and are turn fighting that torque will kick yer arse for you if you are not trimmed right. Especially in the Yak, as well as many other planes

I concentrate on keeping the ball centered as much as possible, via (mostly) rudder trim, so that my forward view is REALLY my forward motion

or else my shots will miss.
Also elevators are critical to keep the nose neutral so that only my stick input cause my nose go up or down. If I feel that the nose wants to "pull" in either direction I counter with some appropriate trim input.
Wings wanting to pull the plane into a bank is the same. I try to counter it with some aeleron trim.
It's mostly an honest "feel" from "time in type." I know the Yak best while the N1K2 or Spitfires the least. I know when to add or reduce trim for any of the axis based on "feeling" excessive resistance to any direction I want the plane to go in. I feel that I have a good grip on most planes performance limits - good enough to be a worthy adversary most times

- that if I was in an F6F that my turn is not very tight and my nose is pulling up because I need to work the elevator and rudder trim.
My thumb gets a good workout

I just add very smal but quick adjustments of trim till the plane doesn't fight my stick input any more. Initial stages of combat from a fast speed to a slow turn fight may need a LOT of manual trim adjustments and vice-versa. And for me it's mostly about keeping that ball centered.
And it's very much like learning the FM envelope on any of the planes. It takes time and patience to learn any planes trim "personality" but when you have it's far far better (and more combat efficient imo) to fly with than using "CT."
(wow. rambled. Well I hope I was at least in the ball park with an answer that landed close to where your question was)
Westy