As already suggested, a good place to start is to replace the stem. What to replace with depends on what you want to achieve. If you want to be sacrilegious you could get a BMX/DH type stem with an absolute minimum forward extension and a steerer tube extender to go with that. Combine that with a North Road bar and you'd be fairly upright.
Or if you want to go from sacrilege straight into heresy, get a riser stem and run it backwards.
It'll look very odd, but it'll work just fine as long as you can remain seated while riding. You'll probably need longer cables to get away with that though. That and a NR bar will put you pretty much in the same riding position as you'll get from a cruiser bike.