Integrated amplifier search

Schiit Bifrost multibit, Schiit Saga pre and Schiit Vidar amp. About $1,650 all together and it would have the small form factor you are after, provide multiple upgrade paths for the future and likely be a considerable upgrade from your present setup. Also get the powered version of the Apple camera adapter (usb3) and if you place lossless files on your phone, it will surprise you. Streaming Tidal hifi from your phone to this setup may surprise the heck out of you. Good luck.

Just a word of warning on going with Naim, you will open up a Pandora's box of  specialty cables and accessories that are not transferable to any other brand. Naim uses their own DIN cables FYI. 
Sound quality aside Naim doesn't play well with others so to speak. you need cables that convert from Naim DIN to RCA for example. So unless you going down that path hard I'd say stay away. This is from my own personnel experience. That's Said its sound quality- ease of use is top notch. 

Glennewdick, completely not true. The Naim Uniti takes regular rca cables in addition to din cables. 

Most of the Naim models until you get into the much higher products use RCA cables. 

In the case of the Naim Uniti Atom, it has digital inputs, rca inputs and takes ethernet in, add to that Aptx Blue Tooth, Goodle Chromecast, and Apple Airplay it is is very unlikly you will run out of connections.

Dave and Troy
Audio Doctor NJ Naim Dealer

Norma Audio has a new half-sized integrated that hasn't made it up on their website yet - the HS IPA-1.  It has options for built-in DAC or Phono as well.

+1 on the Naim Uniti Nova suggestion. I happen to own the Nova for my bedroom setup. It’s highly musical sounding unit. Great all-in-one box solution that does not compromise sound quality and musicality. It is a digital streamer/DAC/integrated amp all in a single box that does not take up much space. Has built-in Tidal streaming app. Very convenient. Great sounding streamer and DAC. Naim makes excellent digital streamer/DAC.

And the Nova has regular RCA stereo inputs, DIN and digital inputs. Even the Naim Statement NAC S1 linestage preamp and the Naim Statement NAP S1 monoblock amps have both regular XLR stereo inputs as well as DIN.

@s7horton
The Naim Uniti Nova will sound better and more musical than your Parasound Halo Integrated. Not in the same league. With the Naim Uniti Nova you will get much better sounding digital front end source components (much better streamer DAC) than the ones you have now. I highly recommend the Nova.
Naim and Parasound aren’t in the same league at all. The amplifier section of the Nova is class AB.
And do not get easily fooled by the Nova’s low power output of only 80 wpc @ 8 ohms. This is a quality amplification current. I’m not saying that your Parasound HINT is bad, no, Parasound Halo line makes very good amplifiers especially for the money but not on the same level of quality, musicality and refinements as Naim.