I used to also have trouble counting when stropping. I used to count some strokes twice (once for each direction) and some once. Now I count slow and strop quickly. Hence the first syllable of the count is the first half of the pass, the rest of the number is the return stroke. It works well for us men who are unable to multitask (counting and stropping at the same time).
This is the method that I use. I only shave with one razor so the count is always the same. I am anal about counting and it seems that sometimes it takes about 10 round trip passes to get in the groove.

Congratulations on the improved shaves. I also found that the lighter the touch the better in terms of nicks and closeness.