I bought Emotiva GR1's to replace the Monolith 1060c's

Apologies for not responding. So, I really like the GR-1's. I don't find them too bassy, even with no tone adjustments. They're comfortable and well-built. I already have the older version of the HE400S, the Massdrop HE4xx, and I agree that they sound better with good electronics. 

My next 'phones will likely be the new Meze $700 cans. I love the 99 Classics as well. 

From the review I read on Part Time Audiophile they sound a bit tilted to the bass that can overwhelm the highs.  If you’re into that sound I guess you’ll be good.  If you’re looking for a more neutral and perhaps more refined sound, I’d recommend the HIFIMAN HE400SE headphones and an Audioquest Dragonfly Red amp/DAC. Both of these have been very positively reviewed, and I have the Dragonfly Red paired with both HIFIMAN HE400S and Arya Stealths and the combo is very good even coming out of an iPhone/iPad over WiFi.  The HIFIMAN ‘phones also scale up when I pair them with my dedicated headphone amp and DAC, which speaks to their quality.  You can get the HE400SE for only $129 or $109 unboxed directly from the company and the Dragonfly Red is $199.  HIFIMAN is a dedicated headphone manufacturer.  Emotiva, well, not so much.  I recommend this only in case the Emotiva products don’t click with you and your music.  If you like what you hear, you’re good.  If not, this might be another option to explore.  Just my $0.02 FWIW, and hope this helps.