Having read thewormman's summery earlier today it set me thinking ...
The main action of Acetone is to aid intimate mixing of the oil and Methanol. This works because Acetone is miscible with both oil and Methanol.
Biodiesel is also miscible with both oil and methanol, probably not as well, but it's available to us at minimal cost and it won't need removing from the process.
I've done a quick test. Nothing scientific just jars of new sunflower oil, very roughly 20% Methanol and a "splash" of Biodiesel.
Gave the mixes a gentle end over end shake in the shed ambient of around 8°C and there was a noticeable difference between the jars with Bio and the control without. No catalyst was included.
Jars were taken inside and sat on a radiator for half an hour and gently shaken again. This is the result ...

From left to right ... Oil and Methanol only, Oil + a Methanol and Bio mix (gently shaken), Oil and Bio mix (gently shaken) + Methanol.
Anyone any thoughts? Can someone replicate the experiment to make sure I'm not being a complete Muppet?