You might be able to find the Focal Clear OGs (white) second hand for £600-800. Most people even prefer its tuning over the Mg. The Focal Elegia also goes on sale at Adorama for $379, which even with a shipping proxy and import tax is still a quite competitive price (see the deals thread). Expect to have to EQ it though, I really didn’t like it stock, but a lot of people do.
Outside of Focal you could try the Sennheiser 6XX which still today is ridiculous value at $240 (shipped to the UK around £230). Beyerdynamic are also popular with their DT880/990 but I haven’t tried them.
A mid tier amp/dac combo like a Schiit Magni/Modi, Topping L30/E30, or the JDS Labs Atom Amp/DAC will work fine with any of the headphones mentioned so far.
I also had a similar ground loop issue using a E1DA 9038D into a Schiit Asgard with a 3.5mm to RCA cable. Given the 9038D is a portable device it wasn’t designed to handle ground loops, and the 2i2 may be similar. You can use a optical/toslink connection, since there’s no ground or power at all to be noisy. If your PC motherboard has toslink out, you could use one of the above DAC recs with toslink in and your existing amp.
I ended up fitting the Asgard with a DAC card, which solved the issue as it has sufficient power isolation on its own.