I struggled with this for about 3 years.
I needed a preamp with balanced out to go between my Manley Snapper monoblocks and my Holo May KTE DAC.
Tried quite a few.
In the end I wound up with a Levinson 523.
Probably outside your budget even used, but it was also outside my budget when I started looking.
It meets your criteria including balance control on the remote, and it is a seriously fantastic piece of gear (better be for the price).
I got mine used at about 1/2 retail.