Scaling amplifier, analog switch, fast response
The analogue switches are a problem in amplifiers like this but you can alleviate things by moving their circuit position. For the feed back resistors have the analogue switches connected to the op-amp output - now, their capacitance to ground is ineffective.

You can also try doing the same with the three Vref bypass switches - try grounding one end of each switch instead of having them at the op-amp node; insert resistors between switch and op-amp i.e. keep analogue switch pins away from sensitive op-amp inputs. It won't be perfect of course but it will be better.