As for checking continuity with a digital meter, I have found that it is not possible--even if the switch is new--Meter is just way too fast to pick-up any "bounce".
On the relay, of course the position of the slugs makes a BIG difference in relay "timing" ! If the slugs are on TOP of the coil, it reduces the length of time it takes to start the armature moving--if slugs are on the bottom of the coil it increases the length of time the armature is held to the relay post, when power is removed. You need to check the Service/parts manual to determine which is correct for this application--and the correct number of slugs installed.
As for moving them--it is sometimes possible very simply, by removing the slug/coil retaining ring--Other times the manufacture "swedged" them together--very difficult to remove, but can be done. Ron Rich