I do not know about flywheel being in a certain spot to start however i will quickly tell you I had a lt 155 before upgrading to gt 235 and my battery was replaced three times in a yr. before i learned that certain lts where shipped out with a stator that was not quilified to do the job . I found and purchased a stator upgrade kit manuf. by Deere to resolve this issue we installed it (a little tricky!) but it worked wonders I have no idea if this helped and dont know if that would resolve your issue probably not but if you are going thru batteries that is definately the issue there . maybe someone else will post with more info on flywheel issue stator upgrade was about 50.00 on ebay it would be worth while regardless .

I'd check ground connections. Battery - to frame, frame to engine, engine to starter motor case.
Do you have a voltmeter?

With a compression gauge, you can see if the release is working. Normally, an engine with a good release will only pump to 85-100 psi, maybe less. If you are seeing big numbers (150psi +), your release is not working.

What "pittg" said is also true. Early LT's had unregulated charging systems (3 amp) that wouldn't fully charge the battery if they were not run long enough or at full throttle. If your engine has a voltage regulator on it, you have the higher amperage (9 amp ?) set up. But regardless, a good, fully charged battery should crank that engine no problem. And running it at full throttle while mowing 30+ min should keep it fully charged even with the smaller charging system.