You've almost exactly described my commute to work. Mine is 6.75, but the two lane I have to take is a 45mph road. I also have an alternate route, but it involves a longer climb that I usually don't like to take in the morning.
Lock my bike to a lightpost or tree out front, change in a bathroom at work, and use the wet wipe method of cleansing, it works. Maybe there's a store room or area inside you can bring your bike? As others said, give a test run on a weekend morning to see how you fare.
As far as the traffic is concerned, as long as you are lit up well, it will generally go around you pretty well. I did my commute for 4 months before I got lights, and noticed a remarkable difference when I just added one blinkie (now I have two plus a 10 halogen up front). Cars really do steer around me now - I think because they actually can see me. The tree lined, two lane road still makes me nervous, but I leave early enought that I beat most of the traffic. On the way home, I take the alternate route, which is longer, but downhill
.
You owe it to yourself to at least give a try. You feel so much better when you get to work, and it's fun to answer the question "dude, where's your car?"
