As I mentioned earlier, the rising pump handle indicates that the non-return valve is not able to hold the pressure in the hose. It is sometimes called a check valve and is a one-way valve. It allows air to travel from the pump barrel and into the hose and tyre but not the other way. You may well find that one of these:
https://www.sjscycles.co.uk/pumps/topeak-checking-valve-joe-blow-sportsprint/ is suitable.
I would call SJS and ask them. I imagine that like my Rennkompressor, it's accessible by undoing a large nut on the base of pump, underneath the barrel. The gauge may well be inaccurate, but for the handle to start rising above a certain pressure, has nothing to do with the gauge. To suggest otherwise, demonstrates a lack of understanding of basic physics, Air does not travel through the gauge, it measures the pressure in a .cul-de-sac' off the hose.
As for whether you need 120 psi or not, that's entirely up to you and concerns nobody else. For anyone to tell you that don't need it or ask what your weight is, is just plain rudeness and arrogance. The fact is you want that pressure and asked a perfectly reasonable question as to how to achieve it.