Many 300B amps would do the trick.
Icon Audio Stereo 300 MKII (300B) which I own is exactly what you are looking for but might be a long time before you see one under $3k. Maybe under $4k used if you are lucky.
It replaces Willsenton R300 which is also very lush but just not as resolving but still really good sounding. New $1.5k used maybe $1k.
Muzishare X9 which I also own 300B but more hifi than lush so not a good fit for what you are looking for but for someone else wanting liner sound then yes. Those are around $2k used.
Willsenton R8 I owned a few years ago. I would have to disagree a little that it is lush. More like bassy. IMHO.