I'm a bit confused by your assertion, that you have found "mixed results as to whether this is actually a word."
If the word can be found in a reputable dictionary, then it's a word. The omission of a word from one dictionary does not make it "not a word" – the omission of a word from ALL dictionaries makes it "not a word" (even then, there are possible grey areas, particularly as the language evolves). Have you ever seen an unabridged dictionary in print?
Moreover, spell-checkers are NOT reliable; spell-checkers flag valid words often (and are notorious for doing so with adverbial forms).
So, yes, sustainably is a word – M-W confirms that, as does COED. It's time to add that word to your spell-checker's vocabulary! My advice is, grab your big-boy keyboard, and don't be so intimidated by those red squiggly lines. ☺ Sometimes you're right, and the software is ignorant.