[Andrew Marchand]

Nevermind. Figured it out based off an old post from 2014 on this forum:

comp("1_MAIN COMP").layer("Profile").effect("Page Scroll")("Slider")
C = comp("1_MAIN COMP");
ctrl = C.layer("Profile").effect("Page Scroll")("Slider");
L = C.layer(thisComp.name);
ctrl.valueAtTime(time+L.startTime)

And for the other:

comp("1_MAIN COMP").layer("Nav Bar").effect("Dropdown Menu Control")("Menu")*thisComp.frameDuration-thisComp.frameDuration 
C = comp("1_MAIN COMP"); 
ctrl = C.layer("Nav Bar").effect("Dropdown Menu Control")("Menu"); 
L = C.layer(thisComp.name);
ctrl.valueAtTime(time+L.startTime)*thisComp.frameDuration-thisComp.frameDuration