See images here.
The bar the new Tioga saddle is mounted on is a bit thicker than the one the original (terrible) saddle is mounted on and won't fit as is.
I can take the old saddle off its bar no problem but it seems like the new saddle's bar can't be removed without removing the clamp. The nut with a slot for an Allen key (it's actually not, it's slightly bigger than a certain Allen key size) is unbelievably solid; it will not budge, which leads me to believe it's not intended to be opened.
I took out the metal bottom inside of the plastic bar with an Allen key. Insides there's a removable spring and deep inside (inside the plastic) it looks like there's another thing to be opened with an Allen key but it's hard to tell. Even if it was, I don't know what kind of tool is able to open something like that down a shaft.
I tried a lot of other pointless things, including heating up an Allen key so it would expand enough to fit properly; I'm pretty desperate at this stage.