Go to Radio Shack and get a $5 multimeter. Read up on how to use it, especially the DC Volts function.
The starter needs voltage across it to spin. Across it means + on the solenoid input terminal and - on the starter case. I like to use 10 Volts DC....use the 20V DC scale, Red on solenoid input terminal and black on starter case.....battery terminal voltage will be present initially.......whatever voltage you measured across your battery + and - terminal......12.75V give or take is a good number.
While holding the leads as you have them, have someone attempt to start the tractor and read the voltage during the process. It will take a couple of seconds to stabilize but when it does....while the starter is still turning, read 10V or more. If you don't have that much voltage it could be caused by your electrical circuit or the load on the starter caused by something binding.
Easy to push the clutch all the way in while doing the above which should eliminate most all mechanical related problems not engine proper related, if it causes the voltage to achieve that number.
Otherwise, assuming the swapped battery was in proper condition to do the job at the time, (a 2-300 Amp battery test to determine that would help.....on both batteries while you are at it....auto parts stores can test the batteries for you), you are chasing wiring problems.
A good place to start is where did you have your battery - lead connected before and where now? Did you move it in the split? If so, that is where I would start looking and you could use your voltmeter across connections to look for the smoking gun. The bad connection will have a volt to several volts across the joint.....like one lead on the battery terminal mounted under an interfacing bolt and the other lead to the ENGINE casting (paint scraped off, nice and shiny).
You could have paint or rust between the contact points that you didn't have before the split........I like to have my battery - lug under a starter mounting bolt which ensures it is in direct contact with the starter case....necessary for good high current conduction.
Otherwise, as can happen, something else decided to fail by coincidence, during your maintenance activity, in the cranking circuit and could be any component, any connection, or resistance that your depressing the clutch failed to catch......tranny shaft jammed in clutch disc too far forcing the clutch disc against the flywheel when it isn't supposed to be....clutch springs compressed, relieving pressure on disc, via clutch pedal.