It's generally the case that GGA requires a bit higher cut-off since you are evaluating gradients of the density, where in LDA you only need the value of the density. But you should not need crazy high values.
Partly it may be due to the pseudopotential, some of the HGH potentials are very, very hard, so maybe if you can try FHI potentials, unless you are already.
The other question is the definition of "convergence". The total energy is not variational w.r.t. the cut-off in ATK (as it is in a plane-wave code), so it will never saturate smoothly, there will always be a bit of wiggling. So maybe if you start from the other end, and do really, really low cut-offs (like 20 Ry) to see what "bad" energies are like, you may find that your results are reasonably converged already at 100 Ry or so (as they usually are!).