I think it may be best to keep this conversation on the original topic which was the TOWELROOT way. People prefer to to use TOWELROOT due to it's simplicity. I used it on my S4 and it worked like a charm, I just wanna root my missus's phone without going into too much headache so I would prefer an answer to my related question, which version of EE UK releases work on TOWELROOT. Otherwise which version should we be using and then towelrooting it.
If and someone makes a separate guided specific to the S4 mini in regards to kernel swaps etc then we can start pointing people to that thread. Right now all the links you posted are for different phones with different downloads not related to the S4 mini. Once you get all your files and test it on your phone I would say it is worth telling people about it.