I agree with these fine folks.
Check with a store manager about the policy on all day parking in the lot. Some parking lots will have posted signs that say "Parking for conducting in-store business only" or something like that. Tell them you feel unsafe coming from where you are riding from and this feels like a safer alternative. Tell them, too, that it would make you more likely to frequent their store after work, since you'll be in their lot anyway! Also, offer to park out of the way - away from store fronts so you wouldn't be taking "prime" parking spots. Don't feel weird about doing it. It's called a "mixed commute" and folks do it all the time.
And...check with your LBS about how other cyclists handle your scary section of road. If other folks do it "all the time" what they may have that you don't is a stronger sense of confidence on the road. Hey, they often say that the secret to crashing a party is to act like you belong. Wave to the horn honkers (all 5 digits, please!) and hold a steady line with your bike. Maybe when you've done your mixed commute often enough, you'll get a better feeling for riding with cars and also for when the peak travel times are on the roads. You can then plan to do the full commute during the lighter times.
Best of luck. Happy pedalling!