Unfortunately, Latios is still some ways away; it seems I have to visit Copycat and get a doll first, then upon leaving the city, the roaming Latios is triggered. I'm only 4/8 on Gyms, and obviously, I have to finish the Pokémon League to continue exploring Kanto, sooo...
I'm going to have to rely on the Action Replay someday to grant myself an Enigma Stone in order to catch Latias at Pewter City. The 3DS version should arrive. Someday. That will let me unlock the Lock Capsule item as well, getting me TM95, Snarl.