I hate video card prices so much these days. My build is on hold until I can figure out how to secure a cheaper one directly (maybe microcenter, frys and appeal to them as a gamer, or going directly to the manufacturer (Hi EVGA!))
So you're wanting to go from a GTX 970 to something better that is hopefully AMD. First things first, the 560 is about 2-3 rungs below the 970 on the performance level. For comparison, the RX560 4GB GPU is somewhere around the GTX 1050/1050 Ti. Or to put it another way, the GTX 970 competes against the RX 570, which superseded the RX 470, which is already much better than the RX 560 4GB.
Now that comparison is framed in your mind, what you want to be look at are the R9 Fury, Fury Nano, maybe the R9 390X (though performance isn't a good leap ahead as the Fury's would be), and anything above those three performance wise. Here's the fun issue: cryptocurrency has led to a giant shortage of video cards available on the market, and AMD GPU's SPECIFICALLY are considered superior for cryptocurrency mining over nVidia's. And yet, supplies are nonexistent for even nVidia; I'm waiting for a GTX 1080 to come down to a realistic price in the low $600s, and they're currently up around $1000-1100! Tells you how ridiculous and insane the GPU market is right now.
So we're in a pickle. Your budget allows for an upgrade that should most definitely be better than the GTX 970. However, the market is going stupid thanks to cryptocurrency and is pricing itself out and above your maximum budget, and I would tell you to NOT pay $1000 for a GPU ever unless you got $$$ to burn. The best fitting card I think for you to try is the RX 580 as that will sit just around your price range, and will be a decent boost over the 970 you got. However, that's a single card and you won't be able to CrossFire them. And the performance hit to actually get two sub $300 cards and CF them won't make it even worth it and just be a waste of your money.
