What I had the most problem with was remembering the position of mittsu, muttsu, yottsu and yattsu, since hitotsu and futatsu I already connected with other words I knew, and itsutsu, nanatsu and kokonotsu are the double sound ones (i+2xtsu, 2xna+tsu and 2xko+notsu). So my method is this:
mittsu and muttsu go together in one pair
yattsu and yottsu go in the other
one pair matches the multiples of 3, other multiples of 4
yo in yottsu matches yo in yon (4), so yattsu goes with 8
u in muttsu matches the only other u in roku (6), so mittsu goes with 3 (there’s no i in san or roku to confuse it with)
Counters for days are similar, 3 and 6 (みっか, むいか) go together, same with 4 and 8 (よっか, ようか). Small っ for smaller 3 and 4, and larger full vovels for 6 and 8. 8 wanted to be like it’s little sister 4, so it changed its や for よ and went with う in place of 4’s っ, while 6, who wanted to be like the cool and unique 1 (いちにち), went with the same い instead. 5 7 9 are the same as before, just that 7 inherited the の from it’s older sister 9. 2 also picked up a large つ, so it makes a nice pattern with つっっつ across 2,3,4 and 5.