At 20 fps and a shutter speed of 1/1000 you cover all of 1/50 of a second with actual images. Statics tell us, that ever once in a while, all the interesting stuff happen in the periods outside that 1/50s.
Birds don't feed in light speed, I'd say waiting until they start feeding, and start shooting then, would give you better results. The D500 does 10 fps, plenty if you time your bursts properly. The alternative is shooting video.
IMHO, I'd try improving my technique until I outgrow my gear or find something that constantly annoys me in the field (all of that is highly subjective) before I upgrade gear.