I saw an '85 Schwinn Tempo in the size range that you are looking for in the LA Craigslist for $75. I own a resto-mod built with this frameset, and it rides rather smoothly. I know that there is ample room for 28 mm tires. 32 mm tires may be pushing the limits.
Here is the link.
https://losangeles.craigslist.org/sf...224110763.html
At that price, you could modify it for the course. New tires, tubes, consumables, and a triple drive train could be had well under your $400 budget.
Have fun with your project and the ride.
Dennis
Edit: Just in case you did not see this on the Eroica California website:
https://www.eroicacalifornia.com/new...ke-on-a-budget