The idea behind Killdry is that when used in a parallel effects loop, you would not want to 'double' your dry signal upon bypass, which is what would happen if the Eventides did not mute.
However as you found out, there is a problem that happens when using more than one pedal in a parallel effects loop. When you try to bypass one pedal but not the other, mute prevents you from hearing the active one.
The solution in this case is to turn Killdry OFF on the Eventides and resave your presets with Mix at 100% wet (TimeFactor) and Intensity at 100% (ModFactor.)
Then you should be able to bypass the pedals individually with no problem. When you want to bypass them both it will probably sound better to use the amp's effects loop on/off switch.