Any updates?
Did it turn out to be the flex plate?
Thank you for your interest and your assistance. I have had to focus my free time on other issues. And, with the weather turning very cold in the Northeast I have paused working on the machine (I have no indoor space to do the work).
Soon after my last post, I removed the starter and had it fully tested, thinking it may be part of the issue. From the look of the starter, it is not very old and seems to have been replaced in the more recent past. The test showed that the starter is working perfectly and not malfunctioning. I re-installed the starter and tried turning over the machine and the initial grinding noise I was experiencing is now gone and it turns over fine; however, now that the machine turns over there is a real racket coming from inside.
I'm not sure why it wouldn't turn over and was making a grinding noise when the machine initially failed, but removing and re-installing the starter seems to have resolved that problem. I can only assume that for some reason the starter became stuck in a partially engaged position and the audible grinding noise was the starter gear chattering against the ring gear. This is now gone and the machine turns over normally.
Turning my focus to the Torque Converter, I removed the fuel tank and opened the cover plate that's on the top of the shuttle. I then turned the engine over and am quite confident now that the Torque Converter is the issue, as the noise I'm hearing is coming directly from this area. The noise is pretty loud and I can hear metal-bits clanging around.
As soon as we get a warmer spell that will last for a couple of days (anything higher than 40 degrees) I will split the engine from the transmission and remove the Torque Converter. My local New Holland tractor dealer can provide an "as new" part for about $300. Hopefully, this is all that's wrong with the machine (at least for this go-around!) and I will be able to put this thing back to some good use.