Amplus shape, (high middle), will pick up and feel lighter than its deadweight, because of the higher bulk of the wood. How much heavier is this than you usually use (in a similar shape or a lower middle bat)?
Could it be on your mind?
Otherwise, sounds like a real keeper, so I'd get a bat maker to take some weight off (back to Keeley, or any maker will do that, retaining the balance etc for £20-40 plus postage).
2+oz is a lot of wood to shave off, and messing with lighter grips won't be of any benefit to pick up etc, despite potentially reducing the deadweight a little.
The other option is to try to dry it in your airing cupboard over a month or two, but it may regain this weight during damp weather/normal use.