At the moment, the Chord Hugo has no equal as far as the sound signature is concern    Frankly, most of the customers buying it is using purely as a DAC for their 100+K hiifi at home    The other plus with the Hugo is offering good enough current for difficult cans like the HD600 to sing.

Balanced is the very last straw in a headphones setup.  The short distance of the cable run will mean very minimal gain sound wise.  In fact, most of the top-end headphones amplifier is unbalance like the ALO Studio Six 

Before considering the option to do balanced in the future with the HD600, you may want to upgrade from the HD600 

Honestly speaking bro, if you willing to spend RM 2-4k for a DAC but still keep the HD600 as your cans, maybe the HD600 will be the bottleneck.
To me, the biggest difference in sound comes from the transducers, be it headphones, iems or pseakers.
If you like HD600 sound signature, maybe you can try auditioning the HD800, AKG 812, HE-560, etc.

I did audition Yulong DA8 but it doesn't have balanced headphone out.
I tried it with my HD800 but to me the amp part is so-so only, so did not proceed further.

I plugged the Roxanne direct to the 3.5mm AK100II jack as I values total portability.
I tried the 2.5mm balanced out but the sound to me just lacking the dynamic, maybe because AK100II balanced out has less power to the single-ended, as opposed to the AK120II and 240.

I have not tried the JH11, so no idea about the sound.
As for the 13, 16 and Roxanne, truth be told I much prefer the 13 sq over the other 2.
I jumped on the Roxanne due o the 2013 Black Friday discount but the waiting period of 8 months for the carbon fiber ciem left a bad taste in my mouth.

SQ wise, the Roxanne is a bit warmer compared to the 13 due to the smooth high and thicker mids.
The 13 sounds energetic, and almost neutral except with a bump-up mid bass. The treble is much clearer, with morr sparkles compared to Roxanne.
The 16 has too much sub bass for my liking, making it almost sound like a V-shape.

Yulong DA8 is actually more on DAC. The build in amp can't really drive headphone like HD600 or K701. Even a RM500+ Cayin C5 portable amp is better than it. So I don't suggest using it as a DAC cum amp.

But it is indeed a very good DAC. It has balance line out for DAC. To get the whole potential out of it, you should pair it with a decent desktop amp.
If you want a full balance system, then can get a full balance amp.  But that might be over your budget.

One of the best combinations I have for HD600 is Yulong DA8 + Lafigaro 339 with upgraded tubes. (total budget around RM7K, excluding upgraded power cord, usb cable, rca cable and receptacles). Lafigaro amp is single ended, but with widest sound stage that I ever heard even compare to higher range amp. It has the typical tube amp sound, warm and rich with good ambience, with good dynamic as well. HD600 sounds very open, detailed, and musical, which makes lafigaro stands out from the rest for HD600.

You can also consider getting their brothers, D200 + Lafigaro 332S. D200 also has balance output and support DSD.
Yulong D200 is more direct sounding and have strong punch at bass compare to DA8. DA8 has wider sound stage, smoother and more musical. Both are clean, neutral, refined, airy.
Other DAC at around the same range, you can also consider Aune S16 with use the latest DAC chip AK4495S from AKM and Matrix mini i pro.
S16 has a stronger build in amp among the rest and can last for a while as a DAC cum amp. But still can't compare to a pure amp.
Matrix mini i pro wise, has very analogue sound, smooth and more on the mids.

If you prefer a DAC cum amp with balance system, I suggest you to consider Audio-GD NFB28. All the models of Audio-GD with ES9018 DAC chip supports DSD, so you can check them out. Audio-GD always has very strong output power for headphones.

It's thick with slightly dark background, sound stage is moderately wide but with good depth, accurate with good punch. What I like Audio-GDs the most is that, music becomes so lively, every single track is like listening to a live concert which makes it so special from the others. I was confused and getting headache when trying to mix and match for my Master 9. My doubt is all resolved until I manage to audition Master 7 + Master 9 combo. So REAL!
It's not a perfect system that emphasize on every technical parts of the sound. But it's definitely a system with strong character, special, charming and so musical.
That doesn't mean it doesn't have good details or separation. It just doesn't push them to your face.