Attempt to refurb

In an eBay strike of gold the other week I purchased a pipe rack. As a bonus, I received all the six pipes that were in it. They were all fairly worn and dirty, but one shape caught my eye. Could it be...? Yes, indeed a Peterson System 313!

It was smooth and bleached with lots of paled bird's eye to one side and a metal ring reading "K&P PETERSON'S" and three hallmarks that are kinda vague but could resemble a pentagram or a shamrock, a cat or fox lying down and a lighthouse or a mushroom on it.
On the wood there is "Peterson" in an arch over "...YSTEM" in an arch over "...ANDARD". Parts of the text are gone.

On the other side it says "MADE IN THE" over "REPUBLIC" over "OF IRELAND" over "313".

The P-lip stem is heavily oxidised and a cafe-au-lait light brown color, and has some indentations close to the button.

I'll make an attempt to bring this pipe back to life as soon as possible - keep an eye out for a report...