Too risky
Some bicycle commutes just aren't worth the risk, and this sound like one of those.
I have commuted for five years, and used to accept some of those kinds of risks, but I was foolish to do so. After a couple of cycle commuters were killed here in those kinds of conditions, I reevaluated, and came up with a different route. However, I was fortunate that I had a different route available.
In most cities, you cannot always safely commute from point A to point B. That has to be accepted.
If an arterial road (as opposed to a residential street) has two lanes and no shoulder, or is four lanes with no shoulder and a lot of traffic, I consider that too risky for a bicycle commute. My rule of thumb is, "can traffic smoothly slide past me without the drivers having to take evasive action, or is my presence going to force drivers to alter their behavior a lot, such as slowing down to my speed, or changing lanes? If it is the latter, I know that eventually I will get hit by a driver who is too distracted on a cell phone to notice me.
Even if you have only a marginally dangerous situation in broad daylight, the situation is even dicier if it is dark or if it is raining. Drivers tend to not see as much when their windshield wipers are going.