Of course if the external chain is some arbitrary ledger that can be updated at will by some corporate entity, then these security assumptions do not hold up. What is required is another rule in the external chain that after R permanent Ti blocks have passed, that it is permanent.
Aha, so we just need to have a consensus to have consensus, got it.
You're begging the question. The whole point of this exercise is to make sure that transaction history cannot be rewritten. If you just assume that it cannot be rewritten, then you don't need all this Ti mumbo-jumbo.
Inclusion of Ti does not make it any harder to rewrite the history, as attacker has access to all Ti and thus he will be able to create a seemingly valid chain which references all Ti blocks but is completely different.
I think you've got things wrong, to improve security you need to reference alt-coin blocks from Bitcoin blocks, not the other way around. This is known as anchoring, it's already used in several projects (for example, Factom) and it can make alt-coin consensus as strong as Bitcoin. (See here:
https://bitcointalk.org/index.php?topic=313347.0)