Is there an official way to speed up Elixir?
Yes, others have encountered this problem. At least one poster on BGG (Tim, it isn't you, is it?), posted that the game drags and proposed a Draw 2 Variant.

No, there is no official variant to my knowledge. No variants are listed in the rule books for Elixir or any of it's three expansions. No variants are listed on the designers websites.

I am not sure precisely how your Draw 2 cards/finds is a better solution to just drawing 1 card and passing. You only pass half as often (since you are drawing 2), but how long does it take to Draw 1 and Pass in the first place? How much time are you actually saving?