Hi Daz, I am not sure about the Solex 38 but I have a Webber DGAS which is fitted with a LOVE diaphragm, not all have them. No you are wrong it stands for low vacuum enrichment! What it does is as the engine is about to slow right down and the vacuum drops in the manifold it pumps in a big squirt of fuel like the accelerator pump (it looks a bit like it too on the side of the carb with a vacuum line to the base of the carb) and off the engine goes again. It could be this causing the hunting so disconnect it as you should not need it anyway, block up the tube, and then set up the slow running as usual.
Peter
p.s. the main jets will probably be too big as well as I expect the carb is from a 2.8 or 3.0