Thank you for your trust gentlemen. I hope you are doing well too.
As one of my dearest teachers told me said, knowledge is useless if you don't share it or question it.
Sorry for the late reply I will try to catch up to your questions.
FuryPanda1. No, the frequency response is completely different, you need a specific EQ for GSP 500 Emperor Potara can make it but he needs the Frequency Response chart. Try the Sennheiser One EQ is more similar, both are open backs.
2. Thanks for clarify what you want as an upgrade. Well IMO if you want next level Stereo Mix which most AAA games are tune for, most definitely you need to upgrade to a DAC/Amp, like Mayflower Arc MK2, Fiio K5 Pro or a Schiit Magni + Modi and a $200 or above audiophile headphones. That will be a huge leap but expensive, yet worthy. i.e. Fiio K5 Pro + AKG K702 will give you an extraordinary immersive and wide open stage sound experience.
On Surround...
Soundblaster G6, has a pretty good DAC and the Surround mixes are better than MixAmp plus this device can drive hungry audiophile headphones BUT as owner of the SBXG6 I can tell you is a very buggy device, you can dig on the reddit site to see how problematic its firmware has been, the X7 is very versatile but its audio performance is mediocre for the price, so I stop recommend this device or any other from Soundblaster which at the end is support is dreadful. Notice I had been soundblaster user since the PCI128.
X3 seems to be more for someone who has a PC analog 7.1 sound system, and you are more like a headphone user.
The very best Surround I had, is the Sennheiser GSX1000 that is unbelievable and it seems the GSP600/500 are tune for it. Unfortunately is not compatible with consoles. You can make it work through a PC Audio Input / Output + Mixer arrangement.
Brave99HeartAs I think I explained before, the HD800s are not better than HD660S, this is not like phones. Every single audiophile Sennheiser has different tonality for different needs, HD800S are more open than HD660S and more detail in the high end, is something that you have to try.
Of course if you want to get the best of these cans you need a more suitable DAC/Amp, anything on the $200 - $400 usd, will do the job. THX 788/789 are great and a worthy investment if you want to hear something more besides videogames, where the sound source can be balanced and higher definition. A good high-end amp will never hurt. A high-end DAC is different story, for videogames (24/48000Hz) a $500+ DAC is overdoing it, money wasted.
Audio for live streaming is a complete different BIG topic and Microphones are as interesting and rich as a headphones, another attractive niche with a very steep slop to fall in to the rabbit hole easly, hehehe.
But in short, for live streaming any of these devices will work, they are only improving your headphone sound at the end of the chain. If you are using mixers, just plug the analog headphone output from the mixer to the input of your DAC/Amp and that's all.
What makes it complex is how you set your microphone (or microphones) and other audio sources on the broadcast gear to stream it to your viewers, what type of microphone is the best for streaming, which devices you need, when you need a mic interface or a mixer.
i.e.
My current audio streaming setup is:

TC Helicon GoXLR mixer + Neat King Bee + Mayflower Arc MK2 + Astro MixAmp -yeah, cable are a mess-
My minimalist setup is:
Phenyx Pro Mixer + Blue Ember + Mayflower Arc MK2 + Android Tablet (sound box)
I do switch to dynamic microphones specially when is raining or I had too much background noise. My top recommendation is the sE Electronics V7, shure SM7B is a timeless classic (just like the HD600) but you need a powerful preamp, a strong boom arm to be able to make your voice sound and feel as you were a guest on Joe Rogan Experience ;-), who turned this mic in to a trend and the majority of the popular streamers are using it.