While the Arcam is undoubtedly good, it depends what speakers you use with it if it will be over the top. Denon, Marantz, Pioneer and Onkyo are alternatives and while they may not sound quite as good the limitation is more with music than movies (IMO).
Essentially what you need is a AV Receiver with pre-amp outputs. The outputs from the "front" channels of your AVR connect to one of the analogue inputs on the NAC-N 272; that input is set for "fixed level". If you run the auto-setup then the levels will be balanced all round. You could look at a processor and add a Naim NAP175 (second hand) for centre and 1 set of surrounds (a second NAP155 for a second set) or a pair of NAP100 might be cheaper / easier to get hold of; but you may not notice much improvement. One possibility you could consider if if you have a "simple" setup (not too many sources) is a Oppo bluray or 4kUHD player which has a single HDMI input and variable output - fronts to your NAC-N 272 and get a NAP155 or alternative for centre and surrounds.
An Arcam AVR390 is around £2000 while a Denon AVR-X3400H with similar functionality (albeit without Atmos support and the Arcam has superior DIRAC room correction) is around £600. The small Marantz NR1508 (or NR1608 if you want 7.1 vs 5.1) is a good option for a smaller unit which still have pre-outputs for the front channels.
Ideally you want the front three speakers to match as close as possible - but afaik Kudos don't do any centre speakers so you'll need to find something which matches as far as possible. You can then use your existing KEF Eggs as rear / surround and possible ceiling mounted speakers for Atmos; or get a pair of different surrounds as you prefer.
This is all essentially what I have - a NAC-N 272 and NAP 200 with Arcam AVR400 front channels fed to the 272 and a Cambridge Audio bluray. Complication with it will be upgrading to 4k as I don't feel it really lacking in audio quality... but thats a different story and unrelated to your needs.