Genesis + Spin is a very small cardpool for a cube, the two cycles are 20 * 6 * 2 = 240 unique cards, or roughly 120 per side.
As you know a “regular” cube, such as stimhack, is 320 cards, and there have even been talks of making it bigger. Still, if you make a 4 man cube, that is 160 cards per side (runner and corp), which would mean 1 of each card + an additional copy of 1/3 of the cards.
I have not looked into card types, breakers etc so you might get way too few options on those too is a risk. Agendas for example, there are 23, so you’d need to add duplicates of half of the agendas to get up to the same agenda ratio as for the stimhack cube, this means you have expended a number of your options already.
I think that Genesis+Spin cube is just too small of a pool and you’d need to have a core set minimum to complete a cube, which then takes you out of the premise of as little additional cards as possible. Try again after next rotation…or Core2.0