Option #2: Gate check the third bag?
If you're not EUA'ed and have three bags to check in, how about checking two at the ticket counter and bringing the third to the gate. Once you, or the GA, or a FA decide it's too big to fit in the overhead, ask to gate check the bag.
Or, is this too simple of an approach (from one who never travels with more than a 21" roller and a laptop bag)?