It would certainly seem that a trimmer is a bad idea on the surface; they’re kinda messy in several ways.
The usual technique for trimming resistance (or a voltage drop, or current) to high precision is to put the trimmer in a part of the circuit where it has less influence, and a smaller effective range - generally in parallel with a much smaller resistor.
For example, suppose I want to precisely trim about 100 ohms (more or less). If I put a 10k ohm pot in parallel across a 100 resistor (and assume that I should only use .7 of its range because things work out better that way), I have a range 100||10k to 100||3k, which is 99.0099 ohms to 96.7149 ohms, or 2.2357 ohms total - a reasonably fine adjustment range compared to the nominal 100 ohms.
Pots don’t realistically have infinite resolution. My expectation for trimmers and pots is to resolve about 100 “steps” per revolution, or 1000 steps for a 10-turn. So my 100 ohm trim resolves to 2.2357 milliohms.
But the fun part is that the characteristics of the pot are reduced by a ballpark factor of roughly 100 in this case, so if its temperature coefficient is 250ppm, it effectively becomes 2.5ppm.
A lot of high-end metrology gear uses such techniques, and have done so for well over a hundred years. (How do you balance a Wheatstone bridge to 0.00001 ohms, with switched decades?)
Use a reasonably good pot, to be sure, but perhaps you don’t have to worry quite so much about its harmful effects as it seems at first.