Integrated suggestions

For ~$5k the Simaudio Moon 340 is an excellent integrated.  You can get the onboard DAC and phono stage, which are both very good.  For the price, it’s hard to beat.   https://simaudio.com/en/product/340i-x-integrated-amplifier/

I think the Moon 340iX is quite a lot of amp for the money...it's SS amp and at the top end of your range.  

If you can give it a listen, I'd highly encourage you to audition it.

Not sure what your speakers are but Hegel has a warm sound. Plenty of power for your 4ohm speakers. I would look at the H190 in that price range. Also, you may consider the all analogue Naim NAIT XS3. Great looking slim line integrated amplifier that at 70 watts/channel of class AB is impressive . I have a pair of 4ohm Monitor Audio Gold 100 5g that sound great with both amps. Good luck on your search!

+1 on the Krell K300i (XD).   This is my integrated and it replaced my PrimaLuna HP Dialog.   I liked both, but the Krell is much better sounding in my system driving Exstatic electrostatic speakers.   It has all the input options you are looking for.   It should be in that $5-$6k range for a nice used one.

Accuphase E280

IMO nothing come close in this price range 

Such a beautifully sounding integrated, and powerful enough for you