Before you start spending a lot of money or getting rid of your guitar, try to see if can borrow someone else Strat and see if you find a big difference that may suggest you would want to try to change out the PUPs or get a different Strat.
A good idea would be to take your guitar to a store and try out some other amps to see if you find a big difference and the sound you are after, at least you will know if you can get the sound you want without spending any money at the moment.
Working with what you now have - consider adding an active EQ to your set up. It may let you dial in the tone you are looking for and you can pick up one for $75 to $100. If it does not do the job - return it. I like the Boss GE-7. Decent Demo on YouTube:
boss ge-7 - Google Videos
In the end you may find that your a " Tele Player " nothing wrong with that.
