The OP asked about tracking the activities of a specific vendor for a given job, not overall job P&L. 

Thinking to have a different class for each vendor might be a workaround, but if you're already using classes to track something else, that's not going to work.

QBO should have some way to show a statement of open / partially paid invoices, what's owed on each, and a total open balance for vendor, and be able to have that for specific projects, as well as in general.

This has been lacking for year. When I used QBD, our former accountant had a report I could run for that, but I can't upload that to QBO.