Assuming the two are related (as in the skeg incident), then drop the lower unit.
Could be the dig clutch. With the lower unit off you should be able to operate the clutch by hand with minimal resistance. Could be Teleflex gear selector linkage is just worn, or the idle speed is running to high? On the engine side do the Teleflex cables seem tight?
Drop the lower unit anyway, that tells you what you're dealing with. If it checks out okay, then look at the cables. If they run under deck they could be corroded or simply need adjusted.
Is that with or without VAT?