No one deliberately runs off the end of a runway but performance calcs will very quickly tell you if the potential exists. I had a Training Captain operating as an F/O who stated in his brief that there would be sufficient runway. When i did the numbers from the QRH it said there wasn't when the buffer was factored in. We went A/B medium for this reason:
Edited to add: day to day I try to operate such that nothing I do would make me (or the training department!) shake my head if I read it “in the subsequent report…”. This was drummed into me many years ago, and thus far it has worked just fine, thanks.
On the issue of GS Mini either use manual A/T if you are not comfortable with conditions or put a few knots in the FMS, either way let managed speed look after you but you keep control of the situation.