Chosen Solution

The display restores to normal when pushed on, and even processes the keystrokes made while it was out. But this is unworkable, to continually be pushing on the screen. It’s over $500 for a new display, but I can get a used 2009 macbook pro 13" for $100 to $200. Can I have the 2009 macbook pro 13" display swapped into my 2011 13" macbook pro? Are they compatible? Thanks!

No they are not., different cables and connectors. You’ll have to stick with a 2011/2012 i5/i7 screen assembly But they don’t cost 500$, for that price you can more or less buy the whole Macbook Pro nowadays. Even here on iFixit price is about half of that: MacBook Pro 13" Unibody (Early 2011-Late 2011) Display Assembly