Refined integrated for extremely neutral speakers?

I recently purchased a set of 50's era Siemens 2000 Fullrange speakers from a favorite musician of mine (long story) along with the amplifier he recommended, a slightly obscure German piece called the Abacus Ampino.

The system sounds great, for the most part--I've been using the speakers as near-field monitors and I've never heard clarity like this before at my desk. But the pairing of a neutral amp and neutral speakers sounds a little TOO neutral to me. I have listened to this combo using both a Schiit Bifrost Uber and a Thorens TD 150 as a source, and it sounds a bit clinical, cold, and sometimes just a tad harsh. Not particularly graceful or cohesive. Lykke Li, a favorite of mine, sounds grating in her upper registers. No good.

I thought I wanted a totally clear window onto my music, but I think I want an amp that trades a little bit of clarity and separation for some richness and ease. I listen to a lot of jazz, experimental noise music (lots of skronking), and electronic music, so I'd appreciate something that can handle rhythm properly and won't turn beat-driven music into a haze.

Is this too much to ask for under $1000? I've been reading reviews for days and can't make up my mind! I have almost purchased a Rega Brio-R, Red Wine Audio Signature 30, Redgum rgi35, and *gulp* a NAD D 3020. Any advice? Am I better off saving up for something more expensive, like a Rogue Sphinx?