Good luck in your quest for the right engineer/ studio for your project. I wish you had a space here in Nashville. I specialize in live recordings at gigs or in the band's practice space (I have no studio space.)
I suppose that many engineers get used to the multitrack, overdub, maximum separation approach to recording. It is simpler, though more time consuming, and results in clean tracks. I always overdub the 'real' vocal track after the initial take just for this purpose. However, I have always gotten better performances from recording the bands playing all together in one space. And, the performance is really what you're after, not some "perfect" Nashville thing.
Joe is correct about studios being careful of their reputations: I certainly don't put my name of any recording of which I'm ashamed. But, I also work as a live engineer, and am confident in my ability to make good live recordings.

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"Take 276, you know this used to be fun."
John Entwistle

"Take 276, you know this used to be fun."
John Entwistle