Suggestions for a tube integrated under $3000

You can easily get an Ayon Spirit 2 used for that price... and if you bargain you can get an Ayon Spirit 3 new for very near that price.

The Ayon is a wonderful integrated

And put a pair of 5ar4's in place of the 5u4's at the rectifier position and this amp really opens up (more transparent with improved bass).

Chuck

Some good recommendations already. Have you thought about something like the MastersounD KT88 or EL34 amps?

A real bargain would be the Aronov LS-960I if well maintained, and about $1200 pre-owned.
It has a most natural, musical character, together with the best ability to optimize bass accuracy and extension anywhere near this price range.

buying a Cayin or VAS is a must, great sound, great value. I own four of them, never a problem. Consider buying used if you can do a pick up, for cash.