I would dry the stevia and freeze the basil. Hang small bunches of stevia in a well ventilated area and store in an airtight jar when completely dry(or grind dry leaves into powder). I have not used a dehydrator for this so cannot comment on that method.

Process basil leaves with a little oil(or make your favorite pesto recipe)and freeze in usable portions. Some use ice cube trays, I just press the paste flat in freezer bags and break off what I need throughout the winter. HTH

You could do both I had many leaves that I freeze dried took about a week a batch I think

I think it depends on how you plan on using them will you be using them as dried herbs? Or will a little extra water be ok? I've heard you can make a paste with basil and a little oil and freeze that for use too

Another thing to keep in mind in my experience unless stevia gets a chill in spring it wont flower so depending on where you are if you get hard frosts it won't make it to next year left outside

The dehydrator method depends on the dehydrator you have mine only has on (plugged in) and off (not plugged in) it requires a bit of watching

I have read that drying makes basil lose much of its flavor.

Basil is best used fresh..Not only does drying make basil lose much of it's flavor, but when air-drying, because of it's high water content, it will most likely mold..

Freezing, according to this link, is one of the best ways to preserve it, and can last 2 years ; http://lifeonthebalcony.com/three-ways-to-preserve-basil

For the stevia, you should make a syrup out of it ; http://theherbgardener.blogspot.ca/2009/08/make-stevia-syrup.html

Why not just grow some basil indoors during the winter in your kitchen window or on your kitchen counter w/ a little florescent grow light? It is easy to grow some parsley and the basil indoors. If you get good enough sun in your kitchen window, you wouldn't need a grow light.