There will be an answer to be found
Closer and closer all the time.
So far, with a combination of Google Translate and digging through bibliographies, I've found:
1) The Soviet 12 Air Army (along with the 9th and 10th) supported Operation August Storm.
2) One Fighter Division from the 12th Air Army (less one regiment) provided air support for the soviet 39th Army (Manchurian Invasion)
3) The 12th Air Army's Fighter Divisions were:
- 190th Fighter Division
- 245th Fighter Division
- 246th Fighter Division
4) Of these, the 190th and 245th were equipped with P-63A's in regimental strength
Conclusive? No; this is only a "they were there" item but there are a lot of other references I haven't even touched yet. More work to do. Sources include G. Mellinger "Soviet Air Forces 'Autumn Storm' Air Order of Battle", D. Glantz, "August Storm: the Soviet 1945 Strategic Offensive in Manchuria" and Pobedo Vnotchenko, "Victory in the Far East" - in russian, of course.
Additionally,
"Air cover and support for Shimushu (Kurile Island) landings were provided by the 128th Fighter Division, their 888 IAP had the P-63 Kingcobra..." - G. Garrido "Aerial Actions Over Kuriles (August 1945)
Interestingly enough, the Kurile islands were a major source for P-63s for modern restoration as the Soviets basically abandoned them there in the mid to late 1950's. Hmmm, wonder how they got there?
Further research includes (if I can find copies and translate):
1) Novikov, A. "Voenno'Vozdushnye sily v Man'chzhurskoi operatsii" (The air force in the Manchurian operation]. Voenno-istoricheskii zhurnal [Military history journal], August 1975:66-71.
2) Sykhomlin, I. "Osobennosti vzaimodeistviia 6-i gvardeiskoi tankovoi armii s aviatsiei v Man'chzhurskoi operatsii" [Characteristics of the cooperation of the 6th Guards Tank Army with aviation in the Manchurian operation]. Voenno-istoricheskii zhurnal [Military history journal], April 1972:85-91.
It's only a matter of time until somebody finds something conclusive. Of course, it would help if I could read russian.