You gave up on the 10684 without checking further to see why it quit? Read my suggestions on that thread. Its a better mower than a 10604.
'2 bail system'? It has a bail for the engine/blade control and one for the drive. Most manual drive mowers have the same.
Its Toro 'Variable Speed' and its my favorite. Basically the same as 'PP' except you control it manually. And when you release the bail, it instantly becomes a push mower for unrestricted pull-back in short push-pull operations.
You 'feather' the drive to go slower and squeeze it all the way for max speed. The 'Insight' mower you have also was available with Variable Speed, as well as many other Toro/Lawn-Boy models.

Thanks Saxman! I did go buy the new machine but haven't given up on the old one yet. My daughter and her husband are in the process of buying a house. I have about a month before they move in so I'm going to go get a coil for the old Lawn Boy and try to get it running so I can hand it down to them.