The problem could be down to either pickups or wood. Barts can sound woolly, unfortunately alternative pickups will cost to try out unless a luthier has a spare set lying around that will fit. If the wood is the problem, fitting a new set of pickups isn't going to make a lot of difference. You're not going to be able to realistically change the neck woods and new wings will be expensive and relatively ineffective. A new fingerboard from maple or ebony might introduce more 'snap' though, along with stainless steel frets, again costly.
I think you need to be really clear on what the cause is before you spend money though.