Automated stirring in a domestic kitchen

I'm currently making 9 litres of quite thick lentil soup in a 10 litre stainless steel stockpot. It needs to simmer gently for an hour or two. Despite the sandwich base and my weakest gas ring on minimum*, it needs stirring every few minutes or it will stick, and soon burn.

I've found this with other similar soups too (e.g. split pea and ginger) and dal. What they have in common is that they're too thick to convect properly. Today's is worse because I'm making it extra thick thicker for further dilution to serve about 40 people. Small batches can be done n my 3.5 litre slow cooker, though even in that it can stick.

Because this cooks for quite a long time, I need to be able to get on with other things, not all in the kitchen. So I wondered about solutions for automated stirring. In small vessels in the lab, for example, there are magnetic stirrers built in to hotplates. Is there something larger for use at home, whether a product (perhaps something that could be repurposed), a DIY design, or something I haven't considered.

* _{I have a flame diffuser, but it's a bit small for the pan and couldn't be trusted to take the weight. A diffuser that clipped under the pan supports would be interesting, like the wire gauze sometimes used with bunsen burners.}