Ticket and tow if you're parked more than a foot away from the curb. That would solve 99% of the traffic issues. If you can't park near the curb, then TFB, don't park there.
Really, I'd like to see more ticketing in general. Throwing snow into the street is unacceptable, yet I see people doing it on every block. Clear your sidewalk the proper width and to bare pavement, or get ticketed every day.
Perhaps a portion of the snow related ticketing could go towards the snow removal budget. Then we could afford to buy fancy snow melters, and maybe provide public salt.
I also agree with the above on the odd/even thing, or keeping street cleaning in effect year round.