Don't forget you probably need 0 and 270 degree shifts as well but you can get those from the other flip-flop output pins.
The stability should be good but you will have to be extremely careful to prevent any noise or hum pickup on the resistor wiring. If you use a vaiable resistor for tuning, use a good quality one with low temperature coefficient.
Not sure about the SBL-1 drive levels, the spec (which I don't have to hand) probably doesn't mention driving with a square wave. In a situation similar to yours I have used CD4066 switches as mixers and even simple diode switches, they are quite happy with logic level drives.
Brian.