Getting enough neutrons to get to where the most stable nuclides are expected to be is a major drawback to the current techniques being used, besides the very small cross sections. Getting to where the most stable Superheavies are expected to be (e.g. Ds-290) with current methods is virtually impossible, even if radioactive beams with suitable intensity become available. Ideally you need a mechanism in between slow netron irradiation and uncontrolled fast neutrons, such as from a atomic weapon detonation. Unfortunately we know of no such method currently. Since they have no charge and free neutrons have short lifetimes, they can't be stored and used as projectiles. This is why we have very little data on neutron rich heavy elements.