I don't know where material costs fit in this budget nor the number of sheets on the roof but I'd suggest to seriously consider replacing all the sheets on the roof with 1/4" CDX plywood. You will get better adhesion for any product you use and can be comfortable that it is all new up there.
If I wished to avoid using the typical membrane roofing products, this is what I'd do: Install new plywood sheets, fill all voids and joints with a patching product, prime with a latex primer, paint with a quality latex/acrylic paint, paint with one of the acrylic roofing top coats like Hengs or other. I would also cover the roof with a plastic sheet or quality tarp both before the pergola is built and after. Some members have topcoated with bedliner or even had the roof recoated with purpose supplied roofing material. The stuff is not cheap and results can be mixed, depending on material and professional installation.
One way to stretch your restoration budget is to use a Habitat for Humanity store or get paint through a neighborhood recycling center. I have a recycling center close to me that stocks hundreds of gallons of leftover paint, varnish, and various cleaning supplies. I haven't bought any of that (for my own use) in years.