I just had a similar experience with my 16 hp Briggs garden tractor and what I found to be the problem defies logic. The battery read 7 volts cranking. I boosted the machine with a larger battery (car). Still very slow crank. I then boosted directly to my starter and it cranked well. I then thought bad connections, solenoid, etc. Remembering the 7 volts cranking, I put in a new battery and problem solved. The dilemma is why didn't it work when I first boosted it? I kept my old battery as I want to test it for a short.
Again I have to logically explain this.
I guess my recommendation is to use a known good battery with the old one disconnected.