TomGeorge:
I have not seen encoders multiplexed and because you need to look at two encoder outputs together and scan them all I'd say its not possible.
However if you give up the idea of a 360 rotary switch and use a 3 position momentary rotary switch that only turns one position left to count down and right from central position to count up, then this can be scanned and arduino eprom used to store the equivalent of the original mechanical memory.
The apperance would be of the original switches, but they only turn probably 1/4 turn clockwise and counter clockwise from a central position, ie 3 position rotary momentary switch.My ten cents worth.
Tom.........
Well, you mentioned 3 position momentary rotary switch, what if I turn more than 360 degrees and repeating a lot ?