One way to accomplish this, and to alleviate a major hassle for summer tourists, is to implement congestion charging on the Maine Turnpike during peak summer weekends. Tolls should increase according to traffic: if traffic is light and moving smoothly, tolls should remain at 60 cents; if traffic is heavy and congested, tolls should increase to whatever price will discourage too many additional motorists from using the highway - for relatively price-inelastic weekend travellers, this price could get as high as $10, or even higher. This policy would not only alleviate traffic on the Turnpike (drivers would be more likely to ride the bus or a train, or to travel during off-peak hours); it would also generate revenue that could be used to relieve other taxes, or to bolster alternative transportation like Amtrak's Downeaster.
To be really effective, variable pricing should also apply to Maine vehicles - after all, locals have better knowledge of alternative routes, and we generally have little reason or desire to travel on the Turnpike on summer weekends. Still, to make it more politically palatable, the Turnpike Authority could allow a 50% discount for Maine vehicles when traffic drives the tolls beyond a certain point (like $2).
Unfortunately, any sort of variable pricing policy is currently illegal, since the state legislature passed a law that forbade peak-hour price increases right before the Turnpike Authority was to begin an experimental pilot project in 1995. But that was 12 years ago: we've now seen examples of how variable tolling can succeed in places like California, Houston, and (on a larger scale) London and Stockholm.
In 1995, the Legislature reacted to concerns that tourists would be "insulted" by increased weekend tolls. But what's really more insulting: a $10 toll (that's the going price for driving in and out of New York City, by the way), or a five-hour traffic jam? I'm pretty sure that most of our tourists would prefer the former.