... I'd probably posit that (one of) LA Pan's best early-game solution to elephants would be a small screen of units up front backed by a handful of dryads spamming tunes. Tune of fear, in particular, should be pretty ruinous to a squad of elephants, and growth is more or less tangle vines or vine arrow, but actually useful

If you can get in range, anyway, which becomes much easier when they're coming right at you. Dryads on tune duty is pretty useful in general for LA Pan, methinks, if you can get a handle on scripting them right.
Could also nab alt 2, bring along a pan and some minotaurs, and enlarge some critters up to no-sell trample size. Pan on panic duty would probably straight-up negate 'em, too -- if you've got const-4 and a D random pan, you could just forge up some skull standards and stick 'em on whatever, as well. That's one of your better things to be doing with non-caster commanders regardless, heh.
Really, anything in general that hits elephants in the morale is a good way to just make them go away. With rare exceptions, their morale is just kinda' terrible, plus when they rout they wreck the enemy as well. S'good stuff.