Starfires - like all Guilds - played really nice, and the Hagstrom pickup gave a much more even tone than a Gibson mudbucker. They couldn't do a mudbucker, but they came a lot closer than a Fender to pumping out that fluffy bottom end. Guild were feeding them to the Lovin Spoonful. I don't know about the guy in the Byrds. So, with classic comfortable EB-2 looks, and more flexible sound, and I am pretty sure they were cheaper, they moved.
As far as the Thunderbird, they were on TV with Zal Yanovsky, and in the middle of Electric Mud. Buddy Guy played Starfire guitars almost exclusively for years.