You will want to use a 1/8 foam for sure. I'm supprised to hear that the molded foam shifts. The foam has a raised area to rest in the channel of the rim. You might try some rubber cement on the inside of the tire to bond it to the foam but this can make the foam seem harder. The Proline foam is smaller in volume than the Panther so that might help too.
"I have no idea what you're talking about, so here's a bunny with a pancake on it's head."
In mind and body, we're all heading towards old age. It is slower to go by bike.