In this part
http://ilpilot.narod.ru/vvs_tsifra/gl_3/index.html
it is possible to see the detailed composition of the VVS-VA's on certain dates broken down to a type-level like Yak-1, Yak-7, LaGG-3, etc.
Other chapters do have data for the phase late 1943-late 1944, but this specific and very interesting one does not. Is it availabe that data somehow? Maybe elsewhere?