I'd keep the omegas for now maybe adding a sub or two to flush out the bottom end and sound stage. I've had a set and they can do some great things.
your amp is definitely the limiting factor here. If I was you I'd have a look at Schiit Audio for new tube Preamp and SS amp easily in your budget. I'd suggest a freya + and AEGIR 2, would be a nice improvement and well under your budget.
Another option would be the rogue audio Cronus Magnum III tube integrated, you can find these new in your budget and use well below.
Cronus Magnum III (rogueaudio.com)
Schiit Audio: Audio Products Designed and Built in Texas and California
many other option so do some searching on here and US/Canuck Audiomart.