The engine from the 6216 should bolt right in your tractor. Any briggs opposed twin motor would probably fit.
Measure the voltage while jumping with the cables. The battery may have a surface charge of 12 volts but not enough depth of charge to crank. These motors take a lot of starting current.The voltage at the battery was 12 volts. I put the jumper cable on each starter and both were very slow. So i either didn't have a good enough contact on the starters with the jumper or both starters are bad.