I doubt that the Anatolian and Tocharian branches split before R1b IE crossed the Caucasus. The linguistic distance points at a separation just before IE languages coalesced in the Yamna period. How else would Anatolian and Tocharian languages have vocabulary for steppe-related terms, chariots, and even Uralic borrowings ? In this regard I completely agree with
David Anthony's new paper.
The scenario that makes the most sense is that the Anatolian branch descended from the pre-Yamna steppe people who invaded the eastern Balkans (Gumelniţa–Karanovo), while the Tocharian branch descended from the pre-Yamna steppe people (Repin culture ?) who migrated to the Altai and founded the Afanasevo culture.
I am not as sure as you that Anatolian and Tocharian branches lacked R1a. There is enough old R1a in both Anatolia and the Altai to suppose that they were both R1a and R1b.