Or could it be that the LA4 revealed a “sheen” inherent in either your source or amplifier? I suggest this possibility because I had that very experience with the LA4 until I upgraded my source (to the Electrocompaniet ECD-2).
I was telling the person who bought my LA4 today this same thing. If you hear a "sheen" or some other nastiness first assume it is another component. I replaced the LA4 with the Benchmark HPA4 preamp.
I did this when I was trying to figure out how to drive the Yamaha NS5000 speakers. I like to use the LA4 preamp to figure things out because I feel it is not going to mess up anything.
After figuring out what amp and DAC to use with the speakers. I was getting a bit of that sheen and fatigue in the sound. I tried 2 different WyWire speaker cable, Benchmark speaker cable, and Audience AU24 SX speaker cable. All were giving that sheen or gremlins but at different frequencies.
I bit the bullet and bought Audience FrontRow and that eliminated that bit of nastiness. The LA4 did what I needed it to do. Let me hear my other gear.
The LA4 also plays nicely with about a dozen amps I have used it with. Just love this preamp. If I did not want headphone support in my big system preamp, I would have kept the LA4 and sold the Holo Audio Serene preamp. I would have been very happy with the LA4 and HPA4 in my 2 systems.