If your keyframes are on your layer in your 20 minute comp, and your layers run for the length of said comp, you can keyframe the opacity/position of one with this expression in both properties;
maxOffset = 250; // frames
seedRandom(index,true);
offset = framesToTime(random(maxOffset));
valueAtTime(time-offset)
Though you could get double ups and it will get messy.
If this animation is something that can sit over the top of your comp, I’d render one instance of it out, along with your final 20 minute comp(without your 4sec comp over it), and randomly place it over the top in Premier. You don’t want to have to re-render something that big if something’s in the wrong spot.
Hope this makes sense,
Good luck