As @lordmelton wrote, the break-in of your Musetec is usually not in a straight line. Just keep listening and it will get there. There are some very fine, and expensive, capacitors used inside and I think those are the components that take time to sound absolutely right. I would not use the Musetec straight in to your amplifier section. You have a great integrated and you should use it for all it’s sonic benefits. Especially at low volumes, you will be sacrificing too much SQ.
The Equi-Core "power conditioner," as you probably know, is not a power conditioner in the usual sense. It does not create new power, like the PS Audio units, nor does it "simply" filter the AC line as do virtually all the others. It changes the AC power lines in an unique way, supplying live power to the otherwise neutral line. Instead of the component receiving live, neutral and ground lines, it gets two live lines and a ground line. So it is possible that a particular component may not take well to that--I don’t really know. My suggestion is that you consult with Equi-Core, perhaps referring them to the informational page at Musetec to see if there is anything there that might not look friendly upon a "live" neutral line. Given that the Equi-Core is such an odd bird, I’m not sure that Musetec could be of any help. However, given what you have written, I would keep the Musetec away from the Equi-Core.