The mini game idea and the one currently implemented seem solid since it'll give the player a bit more control of the stat outcome. I assume it also means more time on animations since you won't need to draw up another event every singe time a stat levels because the same mini game could instead just have a different outcome based on stats. Might get repetitive though so I'm guessing you plan on a new mini game every couple of stat levels if you choose this system.
On the other hand, actions that can always be used (like rest or move residence) to ensure or increase the chances of certain tiles appearing is an option if you wanna buckle down on the current system. Something like beg the boss for more shifts with an under the desk blowjob, prepare a camera crew for dealing with zombies, drink cum for protein, etc.
Either way, I look forward to it and please add cumshots.