yeah Lorkhan is a difficult concept, especially with all the contradictory in-game lore books.

Personally, I don't think the Thalmor really care about the worship of Talos. They just chose him because they knew it would throw a huge wrench into the structural integrity of the empire. "Divide and Conquer" as previously stated. It was just the most convenient method to that end that they could come up with. Typically the "high and mighty" Altmer could care less about what the "petty rabble" worship.

Especially since both sides can end up being correct at the same time. Schitzophrenic godheads don't lend themselves to a universe with great consistency.

This is a very good point, but it needs to be expanded upon.

The godhead is the central entity, idea, or concept of the TES universe. It is all that is, everything is a tiny part of it.
It dreams and it does not know it is dreaming. It is not self-aware, as such.
To understand itself better it first split into two and these later became called Anu and Padomay.
Then it split again and these are the original spirits, or Et'Ada.
It has a tendency to split itself into ever smaller parts or subgradients and only sometimes, like Talos did, do they join again.

It does not know it is dreaming and no-one in creation know it exists, not even the gods.
Only, when a person achieves CHIM*, a higher state of being, such as Vivec and Talos have, they understand they are a part of everything and everything is a part of them. The trick of CHIM is to achieve it while loving creation and especially yourself enough not to lose your personality in this deluge of understanding. Most that are close to achieving CHIM fall into this trap and, what is called, zero-sum out of existence.

There is a step above CHIM called Amaranth which is a concept even harder to grasp, but it involves the godhead waking up and loving his children. Or achieving to be the godhead and loving yourself.

*CHIM is an Ehlnofey word and they are written all in caps. It means starlight, crown, change. As someone recently said on the lore forum 'The word is an anology of sorts. Like calling a smart person "bright." It's not a literal truth but not an accident that this word was chosen'.

The thalmor are hoping to draw the empire to skyrim while making inroads elsewhere