The truth is CCP actually did not get that much help from the Russians. The Russians had to literally kick the CCP out of major cities in North East and turned half of North East to KMT in exchange for Chiang's recognition of independence of Outer Mongolia. CCP was able to conquer NE before KMT did simply because it took time to transport KMT central troops from South West to NE as you correctly stated.
CCP's success in NE was partly or largely due to the successful land reform in North Manchuria and thereby won the suport of the poor people.
Oh, on the book CCP was supposedly to acquire or had actually acquired weapons such as heavy artillery, warplanes, and warships from the Russians. Haha...