First off, I think our terminology is different so lets get on the same page there. What you are calling drying we call color curing and there is alot more to it than just letting the leaf dry. It is the most critical part of the process. Mess it up and you end up with garden mulch. What you are calling curing we call kilning which is nothing more than speed aging the already cured leaf. This step replaces letting the tobacco naturally age over time. (About a year to make it tasty) Kilning reduces the aging to about a month to six weeks. Kilning is optional if you don't mind waiting for the natural aging over time.The flavoring comes last and is entirely optional. Most people here do not flavor but enjoy the natural taste of the tobacco and control that taste through blending different varieties. Some people do flavor, but we'll save that for another day, let's concentrate on your next step which will be color curing.
You can harvest by priming. That means pulling each leaf when it is mature. Or you can whole stalk harvest, which means cutting the entire plant when most of it is mature. I'll let someone else weigh in here. Whole stalk harvesting some of your varieties may actually help slow down your quick drying problem. There is more about that here:
http://fairtradetobacco.com/links.php?ab_s=1
You will need to buy a thermometer and a hygrometer to monitor your curing process. The ideal average humidity is around 70%. Over 80% for too long and the leaves will mold and be ruined. Too low an average humidity and your leaves will dry green and be ruined. By average humidity, I mean if your humidity is high at night but low during the day, you will be ok if the average is close to 70%. People in different parts of the world have to approach this problem differently. Where it's too humid people have to introduce heat and air flow. Where it is too dry, like your situation, you have to introduce moisture. This can be done by hanging the leaves closer together, whole stalk harvesting and hanging the plant upside down, suspending towels from a bucket of water, wetting the floor, or a room moisturizer. There may be other methods, I'll let the other guys share what they do.
When you harvest the leaves they are still alive. Color curing is slowing down the dying process by keeping temperature and humidity in a balance that lets the leaves slowly die without molding or drying green. you have to cure and stay away from those two extremes. Most leaves will go from green to yellow and then from yellow to brown.
After turning brown, they need to completely dry until the midrib is crispy. Then the cure is done and you can either bag them up and let them age or kiln them in the refrigerator kiln to speed age them. This is where the crock pot come in. There are several threads on kilning and we will cross that bridge later. Let's stick to color curing and save that crop. This is the most important step.
Now I'll let others weigh in and we'll answer any questions you may have.