Is it possible to splice a new participant into a LN channel factory?
You are correct. It is not possible to get Diana into the Channel Factory without a transaction that closes and reopens with Diana. 

Splicing-in and splicing-out as explained by Decker et al. in the paper you mention is not secure.

Imagine the following situation:



Alice, Bob and Carol spliced out Dave by creating a new Allocation within the same factory, similar to how Decker et al. explain in figure 9 of their paper. Bob and Alice might tell carol that R^2 is the last update of their channel, but actually they updated to R^3, completely invalidating the new allocation. Carol might have accepted payments in such new factory that will never be reflected. For this same reason, splicing in users is also not secure.

Ranchal-Pedrosa et al. refer to this problem as the broken factory, and suggest alternative factories constructions, comparing them, in their paper Lightning Factories.