Atmega ISP programming headers - muxing suggestions
Ideally you would MUX the whole lot, but i understand if this is not feasible.

I think you are right to use the SCK line, but make sure that the disconnected lines are not floating. Crosstalk on a floating line could cause problems. 

The Atmega chips program when reset is LOW. When in Reset, the chip is listening for programming instructions on the SPI port.

Here is how I would tackle it:


Pull all reset lines low together (so the non-target micros dont drive the MOSI line)
Add pull up/down to each SCK line at the chip (check polarity)
MUX the SCK line
Leave all other lines connected
Use 100Ohm resistors in all lines 


The risk here is that the chip in reset will drive the MOSI line, but i dont think it will. Check this first.