Which integrated amp would you pick?

Try the new Rotel 1592 intergrated amp 200 watts per channel

I've owned the Parasound P5 and A23 separates.  They sound pretty decent.  I'm glad the P5 has bass and treble controls.  My speakers need a bit of EQ-ing.  I'd boost the bass up a bit and the treble down a bit.

I don't know about the Musical Fidelity stuff; I've never heard any.

Saying that...I used to have a Modwright KWI 200 integrated and a pair of Legacy Focus SE speakers.  It was an incredible system!  The KWI 200 has a huge amount of capacitance to handle the peaks.  It was a wonderfully smooth-sounding integrated.  Not harsh, not muddy.  I'd play it really loud and it would still sound nice and clear.  Bass would shake the room.

Primaluna hands down. From entry level through the Dialogue HP 

Have you looked into the Ayre units?   That would be my choice

I have the Anthem 225i. I went to it from a Sonic Frontier pre and Monarchy mono-blocks.

It's a no frills unit but sounds good to me, plenty of power for anything I need to drive. I like the simplicity.