Transit Free Visa or Regular Visa - Which is needed?

I'm not leaving airport. I'm picking up 6 dogs from the meat market to bring to US.
I've got LAX - HK - PEK to get to China on Cathay thru American Airlines. Arriving 3:30 pm, July 11.
I've got PEK - Moscow - JFK to get home. leaving 3:30 am on 12th. On Aeroflot.

i'd love to do a transit free to not pay the $300 for Visa and service to get one. But my final destination is the US - and i think that's the hitch in getting transit free? But no one seems to really know. Do you? :)