"Ko" has nothing to do with "Kai Otsu".
The japanese aircraft designation system operates with 3 stages.
Stage 1 is the major modification, such as significant changes to the airframe (Ki-61-II for instance, which had a 10% larger wing area, new Ha-140 (DB-605 equivalent) engine and lowered back for better rearward visiblity). This stage is indicated by a subtype number, officially in Kanji but often written in roman literals.
I will save me posting images of the Kanji names here.
In roman letters and literals, this Stage 1 "major" modification turns a Ki-61-I (the "Tony" we use to know) into a Ki-61-II.
Stage 2 is a large modification that is just not large enough to justify a new major modification number. "Large" means e.g. not just a change in the armament.
Such large modifications were designated with a Kaizo symbol, normally transliterated as "Kai", with the simple meaning "improved".
No other designations but "Kai" were used for the simple fact that there has never been more than one such modification before the next major modification came in.
In roman letters and literals, this Stage 2 "large" modification turns a Ki-61-II into a Ki-61-II Kai (Ki-61 Version II improved).
Stage 3 is a minor modification such as an armament change.
Such minor modifications were designated with japanese ordinals which, written in roman letters, start with:
Ko, Otsu, Hei, Tei, Bo, Ki, Ko, Shin, Jin, Ki, ...
Note: The first "Ko" (A) and the seventh "Ko" (G) differ in Kanji writing.
In roman letters and literals, this Stage 3 "minor" modification turns a Ki-61-II Kai Ko into a Ki-61-II Kai Otsu (Ki-61 Version II improved type 1 into Ki-61 Version II improved type 2).
Got it? Thanks for your attention

Best regards - Mike