It sounds like you clearly know your trans-axle is broken and I'm not here to change your mind, only offer my experience with the X300.
I have (2) experiences working on (2) different X300 lawn tractors that were diagnosed with a broken trans-axle. Both times I found that the splines on the ID of the trans-axle belt sheave wore out and the belt sheave was free-wheeling on the (vertical) trans-axle shaft. This makes it appear that the trans-axle is broken because the tractor will not move in either direction. The only way to tell if this is what happened, is to disassemble and remove the tractor seat and foot pan to gain access to this. The sheave is on the top of the trans-axle (under the white plastic fan).
Then you can see if the belt sheave is free-wheeling on the shaft (sheave moves and shaft does not move).
If this is the case, then a new sheave is about $50. If you find this is your issue, I have pics and step by step instructions that I made while I did this. I can send them to you if you like.
Again, if you already checked for this, my apologies and ignore my post.
Yes, A thank you is in order for Hill-Billy, thanks for the great advice. Can't wait to go buy a new sheave, hope it works. I will still drop the transmission and change the fluid if and when I get a couple of days off.