I personally see no benefit to HPing my liquid soap to the paste stage. To me, it's a needless waste of my time and energy/electricity. Other folks can certainly do it if it floats their boat, but my philosophy is, "Why go to the trouble if it will saponify just fine without the added heat and extra attention needed?". I'm not saying my way is the best way for all, but it is most certainly the best way for
me, a lass who tends to gravitate towards finding less time-consuming, less fussy ways of doing things.
I just whisk or stick-blend off-heat to the emulsification stage/Lawrence Welk stage, cover my pot and walk away. I have plenty of other things I can find to occupy my time than needlessly hovering over a hot pot for a few hours when I don't have to.
Re: dilution: I'm partial to Carrie's method (3bees~1flower from the Dish), which is the canning jar method. Everything is contained in a sealed environment so that evaporation is kept to the barest minimum, and I am better able to see what is going on as often as I like from the top to the bottom clarity-wise/viscosity-wise without ever un-screwing the lid and causing needless evaporation- by just lifting the jar out of the pot of boiling water and tilting it/swirling it.
In comparison, if I were diluting in a crockpot, the only way I would be able to judge how things were progressing throughout the dilution would be to lift the lid and give things a stir, which would cause evaporation over a large surface area every time I decided I wanted to check on things.... which increases the potential of negatively effecting the overall consistency of my finished soap.
IrishLass