Starting sweet potatoes

[IDemo]

I have been attempting to get some sweet potato slips using the method described here. My shoots have grown 9 to 11" high, yet show no sign of developing the small red nodules with roots at the base between shoot and potato. It is getting a bit late in the season to let them continue for too much longer if they are going to need a 4 month growing season, so I'm wondering if I can just carefully cut out sections of potato containing a shoot and plant them directly, or even just plant the entire potato half - or would that result in too dense a thicket of potatoes in the ground?