I'm looking for a word which means that my current solution is a refined version of my previous one, but it is also a combination of my previous idea and a 2nd idea. I found the following question, but it still isn't the word that I'm looking for.
Your idea is a synthesis of two previous ideas. That sounds much like your intended meaning.
I also am partial to @Cerberus's choice of synthesis, but offer a few alternatives:
integration, composite, unification, blend, amalgam