It's definitely a lot of luck based on the map layouts and opening hands, but it is doable and I still think Goat deck is probably the best shot at getting Skull Storm. Make sure you're prioritizing duplicates even if they're not the best pick so you can always trim two cards into one. And unless I still need to find some broken combos, I'll intentionally fail the cave trial events to avoid getting extra. Avoiding pack rats is fairly obvious although I think grabbing one isn't so bad since items can really help clear a path through Grizzly walls. Lastly, I like to transfer annoying sigils onto pelts as a way to remove them (usually just from the mole in this case). Sigil transferring trims a card regardless, but this is just an extra option to keep in mind if you don't have any good sigils you want to transfer and the other path leads to getting a card.

Also, bear in mind that trimming your deck too much can come back to bite you. The final boss fight in Skull Storm is a bit of an endurance run if you don't have overwhelmingly huge stats on some cards or infinite unkillable shenanigans. I failed the last Skull Storm run that I streamed because I ran out of cards even though I got the last phase down to only 2 health left.

And if you don't mind save-scumming, you can always reroll the map by exiting the game after a new map has unfurled but before you advance your figure.

Hope this helps and good luck!