Seems as if you are doing all the right things!
Ive befriended a number of cats who were holed up in bolt holes (I used to foster) by lying on the floor and offering food from the palm of my hand. Messy, byt satisfying when a little face appeared and a little tongue came out for a lick .....
Tabitha Twitchit who I took on full time (she had been a stray) spent a week behind my sofa, only coming out for a hand-feed, until she decided I was Ok. I dont think she pooed once in all that time but she did pee in a tray which I hd let at one end of the sofa. I never saw her drink, either, but the water bowl level had always gone down overnight - more than just evaporation.
When she finally pooed I felt like opening a bottle of Champagne!
I cant see a tiny bit of milk hurting too much - if it makes you and him feel better
I used to leave the radio on - just a murmur - and dim light (actually a plug in night-light)
It all worked out OK in the end - it is a slow business, but so worth it