I don't see any reason to have three transportation legs (home to start, finish to start, start to home) rather than just two (home to start, finish to home). I don't know what exactly you mean by "bike box and other gear that would have to stay at my starting location", but I would try to eliminate all that so that you leave nothing at the starting location. Perhaps you have a hard-shell case you would rather use, but I'd suggest you make do with a disposable box.
Because of high airline bike costs (except on a few airlines), I would generally prefer to ship my bike via FedEx or UPS to the start and home from the end rather than try to fly with it. Most bike shops provide a "pack and ship" service, and this is often quite convenient from your ending location. In many cases, this is a cheaper alternative than flying with your bike. Even if you feel you must use a hard case and fly with your bike, (as ridiculous as this sounds!!) you may find it cheaper to throw your hard case away at the start and buy a new one at the finish rather than pay the airline's bike charge three times.
Do you have some constraints you haven't mentioned yet?