So, I'm going to suggest something that probably seems odd, but fits in with the OPs sentiments and budget. Buy a BSO from box store or online and transfer the desired parts to his Sears. The quality will be about the same.
The front end is will probably be 1" so that's the easy part. The brake caliper may or may not extend enough. But you could just swap the fork if the steerers are equal length.
The crank will be 3 piece, so an adapter would be needed.
The seatpost may or may not transfer.
The rear would still need setting, and the brake caliper is again a question.
But for under $200 you would get: 700c wheels and tires, derailleurs, seat, handlebars, crank and pedals, and 21 speeds of Tourney(edit) that you could also add brifters to.

Or you could just ride it.