You are always restricted by MZFM whether the flight is long or not, so put a small amount of fuel in and you are going to be well short of the MTOM and hopefully the MLM. If however you put a large amount of fuel in, MTOM and MLM is now a factor.

Remember that fuel does not count as part of the traffic load hence it does not affect MZFM. If traffic load remains the same and you add more fuel, you get closer to the MTOM. Therefore to fill the tanks you may need to offload traffic.