It is of course well known that the numbers used to count days are based on the Japonic numerals, but with a bunch of irregularities when compared to the つ-numbers. Compare

1 ひとつ ついたち 2 ふたつ ふつか 3 みっつ みっか 4 よっつ よっか 5 いつつ いつか 6 むっつ むいか 7 ななつ なのか 8 やっつ ようか 9 ここのつ ここのか

一日 is of course just suppletive, so that’s not really interesting. And 三日, 四日, 五日 and 九日 appear “regular”, that is identical to the counting numbers but replacing つ with か. However, for the remaining numerals it’s a bit more complicated:

二日 and 七日 have a vowel change (a→u/o) and I’ve found a source saying that 七日 used to be なぬか (and still is in some dialects). One finds a similar shift also in 二十歳 (はたち) and 二十日 (はつか).

六日 and 八日 meanwhile show some curious other vowel changes (む → むい, や → よう).

It seems as if the 日 counter would be -uka underlyingly but I cannot find anything backing this up, nor does it adequately explain all the irregularities. Does anyone know more?