It's much less expensive to look for other trees of life on Earth, but is there any reason why a second one on Earth would be any more likely than a first one on, say, Europa or Titan?

It might be less likely, as we (you, me, and a couple scrillion of our closest relatives) provide robust competition against any other types of life, which may, as you mention, need different chiralities of various molecules, and may have trouble digesting any portion of our biomass.