You can definitely get a faster bike for the money you're looking for.
A good place to start would be the Specialized Secteur, it's $850 for the base model:
Specialized Bicycle Components
If you get an "endurance road" bike, they're more upright and generally handle bumpy road better.
A crosscheck or touring bike is not a bad idea either, as they're road bikes that can take a larger tire. But they tend to get more expensive.
Biggest question is whether you can be comfortable on a road bike. Obviously lots of people do ride road bikes, but it's easier to find a comfortable position on an upright bike. Still, the road bike is going to be faster and less exhausting.
P.S. If you don't like quick release for some reason, you can replace them with something like this (Delta Axlerodz Bolt On Bicycle Skewers
):
Robot Check
Usually that's just done for "more work to steal" reasons though.