There is no such thing as an "accident". There are:

Failure to yield right-of-way.
Following too close.
Excessive speed for the conditions.

All collisions are caused by one or more of these three things. OK, maybe hitting a squirrel is an actual accident, but in this case the OP shoulders the majority of the blame- he was clearly in the third category by going 20 MPH on a MUP (even if it is legal).

But, in the case of the head-on collision with the driver going the wrong way, the wrong-way driver was failing to yield right of way, so would be mostly at fault.