Heya,
I'll begin by saying, you likely won't be blown away by anything. I think you'll enjoy any setup recommended here considerably more than a pair of earbuds. However, being floored is something that I would say doesn't even happen with a flag ship high end. It depends what you're listening for and how you're listening to it. If you're into high fidelity and you're an analytical or critical listener, I imagine nothing will blow you away. If you're into listening to pleasure music, very casual, I bet a $30 pair of headphones that are very musical and warm will pretty much put a huge grin on your face.
Based on your musical choice, I imagine you're the second type of listener. The pleasure casual listener who is less concerned with high fidelity and more concerned with just listening to something and it sounding musical and good to you. Ie, you're not concerned with accurate reproduction. The HD650 is an excellent headphone for this, it's very warm and musical, dark and bassy. Excellent for chill/ambient stuff. Very comfortable. If you wanted something in the closed variety, I would put you towards the Denon D5000. And if you wanted to save some money and get a very similar sound, I'd push you towards the (open-air) Fischer Audio FA-011. And if you wanted a closed headphone and wanted to save even more money, the Panasonic RP-HTF600-S with Beyer DT400 Velour Pads.
That said, I would not go too in dept on your DAC/AMP choices and instead, focus on the headphones more based on what you listen to and based on how you listen--likely a casual pleasure listener, I would say the DAC is less important here for you and not likely something you want to wax technical about. I might be wrong, that's up to you though. I would not suggest getting a $400+ amp/dac for your needs. I would instead suggest you simply get something that will cover virtually anything for about $200 instead and then put the rest of your budget into some really comfortable, luxurious headphones. I would put you onto the Maverick Tubemagic D1 or the Matrix CUBE DAC/AMP or the FiiO E7/E9 combination, all in the $200ish area. Then use $500ish of your budget for some serious headphones.
Suggestions on headphones that will be powered fine by those units:
Open-air (no particular order):
Fischer Audio FA-011 (warm, bassy)
Fischer Audio FA-002 (neutral)
Sennheiser HD650 (warm, bassy, dark)
Sennheiser HD600 (neutral, bright)
Sennheiser HD598 (bright, forward mids, less bass)
Ultrasone PRO 2900 (metallic, very bassy)
Ultrasone HFI 2400 (metallic, bassy, rolled off highs, smooth)
BeyerDynamic DT990 (bassy, sparkly)
BeyerDynamic DT880 (neutral)
AKG K702 (neutral, huge sound stage, light on the bass)
Hifiman HE-300 (neutral-ish, forward, bright)
Closed-back (no particular order):
Fischer Audio FA-003 (neutral)
Fischer Audio FA-002w (Open turned closed/semi-open via wood back cups; neutral, woody)
Denon D2000 (neutral, flat down to the lowest sub bass, a touch of brightness)
Denon D5000 (warmer, bit more bassy, otherwise like the D2000 but wood back)
AudioTechnica W1000X (sound stage, detail, not overly bassy, wood back)
BeyerDyanmic DT770 (bassy, trebly)
BeyerDynamic T70 (neutralish, detailed, not bass heavy)
Ultrasone PRO 750 (bassy, good mids, bright)
Shure SRH940 (detailed, mid monster, bass light)
Very best,