Inexpensive, neutral-to-warm sounding SS headphone amp?

Thanks, freediver.

I gave up tubes in both guitar amps and audio amps years ago.

I seem to have bad luck with tube gear compared to others and am no longer willing to deal with the headaches. 

I do appreciate your contribution, though!   

Well CRAP,missed the SS prerequisite..Oh well I'm going to post this anyway because you REALLY should consider it...
The amp your looking for is the APPJ Audio "PA-1502" Transformer Coupled,Class A TRIODE Tube amplifier...This amp is specially designed for Low Impedance headphones like your Grado’s & the Planar Magnetics popular today from HiFIMan,Audeze & others..
It has good power out into low impedance & EVERYTHING a good tube amp can deliver like tonal purity & color,spacious imaging & staging & since it’s transformer coupled it has very good bass control & excellent tone & color..You ABSOLUTELY can not get a better amp for your budget & yes I have owned one..If you search head-fi.org & google you’ll find several reviews..

I bought Jotunheim and am very pleased with the results. It seems to be an excellent pairing with the Aqua DAC-- very agile and detailed enough to suit me while still maintaining musicality. I will upgrade my headphones next year.  

Schitt Asgard ii, class A
Massdrop THX AAA 789Audeze Decard DAC/AMP class A

I'm very sensitive to highs, hence my (perhaps) over-concern with straying into fatiguing territory. . . 

Yes, indeed-- the Aqua DAC is on the warm side but my headphones are not...

I will probably try the Jotunheim first, see how I like it.

I had a Creek that was relatively warm.  Aqua DACs are pretty warm so you shouldn’t need to warm of a headphone amp.  

Hi soix--

Thanks for your response. 

I've upped my budget to $400, so now I could afford a Jotunheim 2, for example.

Anything else come to mind??? 
 

Gustard H16 is worth a look if you can stretch a bit, or even better a used Singxer SA-1 will give you that warm Class A amp goodness.  Best of luck.