I think you are definitely overthinking this. If your intent is to book a simple A-B / C-A round trip with open jaw, with the outbound in J and return in Y, this is very straightforward to do. On the United website, simply select each leg of the journey in the corresponding class.

It can also be done on ITA, although it's a little annoying as you need to force all of the booking codes. It is also (generally) true that any Economy fare can be combined with any Business fare to create a valid round trip. There is really nothing special about the mixed-cabin as long as there are fare breaks where your cabin class changes.

ITA syntax would be setting class to "cheapest" and adding the routing spec

to the outbound (assuming UA metal).