You gotta give us more to work with here. HD600 is listed as a 300ohm impedance headphone (let's just stick to Sennheiser's rating and ignore for now the impedance swing by frequency that I've seen mentioned before). Last I checked, 300 falls inbetween 8-455 and the HD600 is an over-ear headphone, so I'm failing to understand what exactly is unsuitable about that. At least regarding the amp I listed, the specs seem fine, it's cheap as hell, and clearly you haven't listened to it, unlike how you've said you've listened to the O2.
So give us something to go on here.
@BobG55 even mentioned tube vs SS and you haven't addressed that either. Heck, we still don't even know what you're calling cheap; cheap is $100 for some people and $500 for others. We can't be of much help just shooting blind here.