The ROgue specs I've read indicate doubling power output from 100 watts into 8 ohm to 200 into 4 ohms. That's not a guarantee but a good omen for getting good performance out of the Manis.
Class D amps require less beefy power supplies in order to do that than most amps which makes ones that do good candidates on paper for demanding loads on a budget.
But the Manis are only 85 db efficient, so yes, ability to go louder and clear could be limited.
You would probably have to go used to do better/go louder. The more powerful MF would be a good choice for that.
Frankly, I think you might be better off going with a used power amp and separate pre-amp with hard to drive speakers like the Manis. Integrateds, especially less expensive ones, tend to not have the beefy power supplies needed for high power and current delivery. Class D integrateds, like those from Wyred maybe, might have the best chance and might be had used.
For separates, you might for example try a d-sonic class D amp used or new and match that to an affordable separate pre-amp within your price range.
I'd shoot for whatever you can find in your budget that features a 250w/ch power amp or more if possible, plus good current delivery ability. That's the main and most straightforward thing to get right first.