Thanks! It's serial number 390174.
I'm working on a couple of issues with it.
1. The prior owner had ruptured hydraulic lines and replaced one of the drives with a drive from a donor mower. That drive seems sluggish and weak compared to the other one. He suggested I add more hydraulic fluid. He also suggested I may need to bleed the lines. He recommended 20w50 for hydraulic fluid but it looks like that is not what Toro recommends.
2. Also, the mower wants to cut off when the parking brake is released. Using the mower with the brake on seems... not good.
He said he thought something needed to be adjusted, but I have not even begun to look at that. I was hoping for a service manual for the "traction unit" but there were hundreds of pages of results on that keyword. I actually reached out to the myturf people and they could not find service info for me. I was finally able to learn the correct (I think) drive belt for the blades.
Any ideas where I should start to look?