I don't know the Hegel, so I can't comment on what sort of level of speaker it can handle. Generally, a well designed speaker will respond well to better amplification, so I'd say explore this route first.
The one thing I would say is that you should audition amplification with the speakers you intend to get, rather than with the R300s. It's no good getting a better amp based on the R300s, only to change the speaker and find it isn't quite up to the job.
Each of the Reference models you list will be a good step up from the R300s, and while all Reference models old and new follow the same design brief, they do sound a little different, thanks to the Concept Blade. The 201/2s are great little speakers, not the deepest bass but certainly doesn't lack presence (think of it as a grown up, far more capable LS50). The 205/2s are my favourite from the old range. These are stunning speakers when driven properly, and will handle literally everything you have to throw at them. I find the Reference 1s, whilst not maybe having the output of the 2052s, are more listenable with rougher sounding material. Don't think that they are glossing over anything though, as they certainly are not - they have inherited this trait from the Blades, which just sound good even with compressed/roughly mixed/recorded material. Each of these speakers will have different requirements from the partnering amplification, but the common thing is that the more you give the Reference models, the more you'll get from them. What source equipment will you be using?
Whichever Reference models you explore, I'd be looking at Devialet, Chord Electronics, Classe, and Cyrus. We've found these work well with all manner of KEF models. All of these have their own sound signature (or not, as the case may be), and despite what people May tell you about a,pluggers sounding the same, I can assure you these all sound quite different. The Classe and Devialet are more flexible in their set up, whereas the Chord and Cyrus are a little more old school in that respect, keeping things simple. Do you have any specific requirements of the electronics (DAC/digital inputs etc), or do you just want a straight analogue pre/power?