I'm working in a field where m=1 and hbar as a semiclassical scale is given as order of N (number of bosons or fermions), i.e. I don't do actual real physics...

But.... a thought experiment:

If a particle experiences time differently dependent to its speed in relative to a frame of reference, i.e. that time experienced is scaled according to its speed. Since speed is definitely not discrete, scaling it with time, even though time in itself is discrete as you claimed, still makes the time experienced for said particle to be continuous, no? Is this not a contradiction?