The Snowie 3000 has a 3/4 hp motor, which has a tremendous surge current needed to start it. I've seen them used with double 4 gauge wires (very short) to deliver that much power when needed. (Once running, it doesn't take that much power.)
I would really, really, really consider buying a 12 volt shaver. The inverter problems are difficult to solve, and you will spend more time fighting it than selling product.
Yes, it's a lot of money to buy another one, but the unit you have can be sold on eBay to recoup some of the cost.