Seems like worth trying.
You may have a better idea when you open it up. With a small pry bar push weights out until you see the heavy spring take up some slack. Is right at the begining, at the near the limit or something in between?
As best I can tell, transfer slot exposure on the secondary side is typically none or minimal. Secondary pump shot covers any delay in supply from the secondary t-slot. I don't know the exact timing of when secondary t-slot comes into play - I assume it is mostly for very high speed cruise or lugging a load when the secondaries a only somewhat open.