I agree with Tvad and Pubul57 that your current speakers preclude most if not all tube amps in your price range.
One possibility is to go to a Class A solid state amp. It won't sound the same as tubes, but may give you some of what you're looking for. I had good success with the Monarchy SM-70 Pro, using two in a monoblock configuration. They'll handle the 3 ohm dip just fine. They can sometimes be found within your budget for a decent pair. Make sure they're of similar vintage so that the input sensitivities match.
David
One possibility is to go to a Class A solid state amp. It won't sound the same as tubes, but may give you some of what you're looking for. I had good success with the Monarchy SM-70 Pro, using two in a monoblock configuration. They'll handle the 3 ohm dip just fine. They can sometimes be found within your budget for a decent pair. Make sure they're of similar vintage so that the input sensitivities match.
David