I must second Dirk's suggestion of screaming frog, great tool and I use it daily, a license is well worth the cost. Although spider crawl of the site will only point out 404's that have are links from an existing page, so if the hosting company cleaned up the not all of these 404's will surface.
One approach I would suggest is run the current 1000 404's in GWT through Screaming frog as a manually added list, (do it in 2 batches if you have the free version), start a spreadsheet of the resulting 404's and start working through that list. Once you have the 404's mark those as fixed as GWT tools set a reminder to check back in a few days and after a few days export the new list of 1000 404's and run these through screaming frog adding the resulting list to your spreadsheet. Keep doing this until you get the 404's errors in GWT down a manageable level.
I hope that helps, good luck.
Open Graph, although is picked up by other platforms, is mainly for providing structured data to social platforms (mainly facebook). Plus, when you view source the open Graph tags do not reference the paragraph that Google uses for the "answer" it uses the intro paragraph which doesn't answer the question. The title is the question, so that is a step in the right direction. The answer is the second paragraph which is not referenced in any structured data that I could see.