Which amplifier (integrated) would you recommend for Monitor Audio PL speakers

I actually listened to it at the seller's house, and it sounded good there.

Also the reviews tend to be positive when I was doing research.

Furthermore, it is/ was the top range of Monitor Audio.

Any ideas for amps?

I think there are two main reasons for the perceived brightness. Reason number one is speaker set-up. 95% of audio enthusiasts don't take the time to learn proper speaker set-up and methodically find the sweet spot. Read Jim Smith's book Get Better Sound for the methodology. And some don't even try in order to appease the wife. 
The second reason is the Rotel digital amp. Class D is getting better and better but a five year old Rotel design is not a good match for the Monitor speaker which will expose every bad tendency of the Rotel. You need a warmer sounding A/B solid state amp. In your price range, I hesitate to recommend a tube amp unless you can find a deal on a used PrimaLuna or Pathos or Manley or similar. 

I'll make it quick, a Rega Elex R might help immensely. You have lots of good advise above to consider as well. 

Everyone must junk their inferior Thiels, B&Ws, Monitor Audios, well, actually all speakers, and buy ATC speakers according to The King of Nonsense.

Oh yeah, and you must listen to rock at ear-splitting SPLs too. That’s the only barometer of a great speaker after all. You won’t be able to hear a lick (just like The King!) after much of that so it’s all good.

Dave

I'd think the Lyngdorf TDAI-2170 or the Mark Levinson No. 585 would mate well with those fine Monitor Audio speakers. They're both clean and dynamic, and could drive them effortlessly.