I don't think you can use this recipe with a standard machine.
Ice cream machines are supposed to only freeze ice cream to a certain temperature (the "draw" temperature) and the rest happens in the freezer. To ensure that you don't overchurn, modern cheap home machines have some kind of sensor for the resistance of the mass, and professional machines have a special type of bearing such that the dasher stops moving at a certain viscosity even though the motor continues turning. Machines in between those two classes (such as home compressor machines in the 200-2000 Euro range) are notorious for having short lifetimes if not stopped before the ice cream has frozen too hard.
I am pretty sure that the sticky mass you are describing has higher viscosity than your machine has been designed for, so you won't be able to continue with this machine.
You could try a manual method (either entirely with your hands or with a hand cranked machine) or go some kind of DIY route and build something to churn for you, using some kind of motor adapted to the task (high torque, low speed). This may not be sufficient though, since a normal dasher design won't be able to exchange the just-frozen mass from the wall with the warm mass in the middle when the viscosity is too high. In the end, you might be looking at either direct freezing (which will still produce something scoopable with this kind of recipe, just not too similar to what we usually regard as ice cream) or high-tech tomfoolery with liquid nitrogen and the like.