I personally would not power wash anything on my bike. But that's just me.
When I rode more regularly, my road bike chain didn't accumulate the massive amounts of gunk you're describing in 150 miles a week. It could be the lube you're using is attracking dust and dirt, making the drivetrain gunk up faster.
I'd remove the chain, clean it thoroughly with and old toothbrush and kerosene - don't soak it, though. (I recommend kerosene because it works as well as anything but is less volatile = less flammable, less toxic fumes). Wipe it down with a rag that has some kerosene on it to remove the residual dirt. You should clean the front rings, freewheel cogs, and jockey pulleys at this time too.
Spray a good quality chain lube on a clean rag till it forms a little puddle, and pull the chain through that section of the rag while lightly closing your hand around it. This should deposit enough lube to reduce friction and rusting without attracking dust. Once a week, wipe it clean with a dry rag, then reapply a light lube.
There are many good lubes out there. Try a teflon-containing spray, which are "drier" than typical lubes and a great friction reducer.
Hope this helps!