I love my Lab12 Integre4 MKII dearly. It costs slightly more than your budget brand new, it has that liquid sensuous mid-range but still muscular sounding. Below $10K there is no better tube integrated amp I think than that.
Leben CS600X and ARC I50 are good recommendations as well and you can't go wrong with them. I have not heard Triode's KT88 integrated yet, but seems like a good value proposition as well.