"big, fat, and solid" sounds like a moth caterpillar. Have you considered either a Giant Silkworm (such as Luna Moth Actias luna or the Polyphemus Moth Antheraea polyphemus) or else some kind of Sphinx Moth (such as the Tomato Hornworm Manduca quinquemaculata)?

Even if those are not an exact match, the shape of the larvae is representative of the entire family.

Jeff

By projections, do you mean something like the ones on these sweetbay moth caterpillars?
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Sherry

Yes. This was a solid green caterpillar. It has two sets of tiny orange projections ( not like a saddleback which has stung me while gardening) on one end, and one tiny orange thing on the other end. There were no stripes, just a seam along the sides near the underside of it. I could not tell which end was front! LOL.

I looked through one site that had 70 pictures of green caterpillars and could not find a match.

It had to be a moth and it was a large caterpillar. I've seen tomato types but don't think that's it.