Ducky Shine 2 TKL and order a separate set of backlit keycaps (Ducky currently has several different colors of their backlit keycaps).
Seems to fit what you're looking for and I'm surprised noone's mentioned it. The lip at the bottom of the board's casing is a pretty standard size, but on the sides it seems smaller than most others as well. Ducky's backlit keycaps are much higher in quality than others you'll find as well. The backlighting has different lighting modes as well brightness levels too.
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Looks nice.
Is the brightness of the LEDs configurable? It would be nice to put the keyboard in low / no LED mode.
I see Ducky has a keycaps page but only see white and black keycaps as an option. Brown keycaps with pink LEDs would be a great combination.
On the lowest lighting setting: in a well lit room you can barely tell they're on; in darker settings you can clearly see them, but they have a soft illumination to them, not a glaring shine.
If you haven't checked, they also have many popular colors for the LED backlighting too.
Ducky has the basic Black backlit keycaps as well as Grey and Purple, but they are kind of hard to find atm because they sell out quickly; I think they have more colors planed for the future too though.