Can one improve Tangletongue fork even further?

I just wondered about the possible consequences of the wording "Forks critical hits" on the spear Tangletongue.

According to many sources this means that the critical hit rolls twice for crit chance, like lucky.
But instead of "just" increasing the effective crit chance, in case of a double crit result, the crit multiplier will be doubled too. In case of 100% crit chance and 400% crit multi this would result in all hits always hitting with 800% crit multi damage.

I hope i am correct so far.

Now for the interesting part: What if the characters projectiles fork into 3 projectiles?!

By using the two nodes of "Split Shot" (75%) and "Forking Projectiles" (25%) forked projectiles would create 3 projectiles instead of only 2.

In the before mentioned case (Tangletongue/100% crit chance/400% crit multi) wouldn't that result in dealing 1200% crit multi damage on every hit?

The tooltip on the "Forking critical hits" would suggest that not to work, since the wording there uses "either" and "both"...

I'm not sure why we're relying on what "many sources" say. The tooltip seems to make the interaction explicitly clear.

It's basically an enhanced version of lucky where if both rolls crit then you get double your multiplier. I don't know why they called it "Forking Crits" instead of "Extra Lucky" or something, it seems really confusing to borrow the word "fork" for something that is unrelated to the other very common meaning of this word in their game.