And one more;
If you calculate the exact per-cent error, then the new gear will need that exact percent correction. More teeth will slow it down and fewer will speed it up
Here's an example;
if you went from 3.23s to 3.73 you might find by testing, that the per cent error is 15%, so you need a 15% change in tooth count. If she's reading 15% high, you'll need more teeth.
If you had a 30tooth; now you will need 15% more or 34.5. From 34.5 ,you would round it to whichever way you want, or to whichever gear you can get.
Then retest and make a mental correction forever after.....