Answer to Animalism Combat

Other than prevents and presses to get out of combat (which gets old really fast), what are good ways for stickmen or similar decks to deal with combat?

Strike: Combat Ends wrecks ANI combat.

You already named the best way for Weighted Walking Stick decks to deal with combat.
Using has the added advantage they can't taste your vitae.
That's the beauty of Gents and Sticks - it deals well with lots of different decks.
Why do you say it gets old?

If you don't mind going to torpor, Undead Persistence Trap is a way to destroy combat decks.

Ivory Bow (until destroys it) is also a good way to deal with it.

I often put 3-4 stunt cycles in my potence decks to deal with Ani combat and breath of the dragon stuff. Incidentally, they also happened to be quite effective against weird stuff like nephandi with molotov cocktails.

But usually S:ce is ok. And if you can deal damage with your vamps, remember maneuvers are scarce in Ani, maybe it's the way to go.

Also, Armor of Vitality tend to work well. I tend to prefer it to Soak because, like Stunt Cycle, it work against less common threats like Ivory Bow, Outside the Hourglass, Molotov cocktail, Dragon's breath.

Torn Signpost + Thrown Sewer Lid

Edit: ... oh, you asked about stickmen: I'd recommend psychic assault and target vitals.