Low powered integrated recommendation

If price is not an issue, then how about Audio Note? Ask @ghasley  about them. Or @decooney 

https://dejavu-audio.com/audio-note-integrated-amplifiers.html

Do you need a remote?

Looking at your quite excellent listed main system, you might enjoy something from Sugden. They've got multiple choices for integrated amps. And there are color options if so desired. The good sound in a compact package was my thinking here. If you'd like to go further upmarket, and depending upon one's speakers for the bedroom system, Gryphon also has a few choices, but maybe less compact. 

Then again, reviewers seem to have fun with the Musical Fidelity A1. 

Best of luck!

Notable well reviewed low powered integrated amps:

• Sugden A21SE Signature Edition 30/40 wpc 8/4ohms
• Lejonklou Boazu 24wpc
• Don Sachs Valhalla tube 32wpc
• Line Magnetic Analog Sound AS-125 18wpc
• Pass Lab Int-25 ss 25wpc
• Leben  CS600X tube 28-32wpc (Genalex Gold Lion KT77 tubes)   
• Luxman 590AXII ss 30/60wpc                 
• Mastersound 845 Compact integrated 30wpc 12/7wpc tested         
• Grandinote Shinai 30wpc 

Rega IO is stunningly good for the very low price, and fits your requirements perfectly. 

Compact, 30 watts, inexpensive, sounds great, and also has a decent MM phono stage.

I use mine in a desktop system with a pair of Chartwell LS3/5As and the sound is remarkably good!