"My source is a Hegel HD12 streaming music from Qobuz via USB."
If that's what you are using for a source, there's no need to worry about balanced operation. Your dac isn't fully balanced. At best, you may notice a slight difference, but nowhere near enough to not go with a single ended component that you like.
The upside here, is your dac has a volume control, and if that's your only source buying just a high quality amp can be a very big upgrade. The biggest problem with integrated amps in your price range is that the preamp section is usually the bottleneck. Its difficult to find a good sounding preamp for 2-3k, let alone finding one in an integrated amp where the cost has to be shared between 2 components. So, if you can't get a good preamp, don't get on at all. There's no shortage of good used power amps within your budget. You can even find a good, high power tube amp like an ARC VT-100 or a VAC PA 100/100. Most tube integrated won't have enough power to properly drive your speakers.