Is there a reason to switch from ultra to high? Also is it possible to get a 1440p monitor and a 5700 in that price range?
In most every single game I have ever played, I cannot tell a differance in visual appearance from High or Ultra. Maybe on specific settings like "Shadows" you see a bit of a differance, or maybe AA. But as an overall for things like "Bloom" or things like "Ambient Occlusion" 90% of games you will be VERY hard pressed to actually see a visual difference unless your zoomed in with a microscope.
Its always nice to be able to play on Ultra at the desired FPS of the user, however High and Ultra usually show MINIMAL visual quality increase, but come with a pretty hefty performance decrease. Its up to you as a user to define wether the differance is so good that you HAVE to have it on Ultra.
As far as trying to squeeze a bit more performance out, have you overclocked your GPU and CPU? Typically a gpu overclock will give about a 8-15% fps increase depending on the game, and a CPU overclock will give like a 4-5% increase in most titles, maybe 5-10% in some others.
If wanting to get a new GPU and Monitor I would suggest something like the 5700 or the 2060 for 1440p. But honestly any monitor thats 1440p and 144hz, and is any good, is going to be about 300-400$ on its own and the 2 gpus I listen are around 270-300 so your budget doesnt look very friendly with what your looking to have. You may be able to find a cheap 1440p 144hz monitor but it will look bad and probably have a lot of ghosting/bad viewing angles/color accuracy.. etc.
But if your only looking to run at 60hz anyways on max settings a 1080p 75hz monitor would be more than enough and I know of a GREAT one for gaming for about 170 bucks. The Asus VG245H.