OK, so my "old Chrysanthemum book" is:
CHRYSANTHEMUMS
for Amateur and Market Grower
by
F.W.ALLERTON
first published in mcmxlix, which is a while back, but I don't expect much has changed in the last 162 years...
I note that wherever the plants are, FW says to wait till January to do anything.
Personally, I follow FW pretty closely here, although I've never resorted to hot water eelworm treatment. I think the tip to bury the stools half an inch deeper is great, the cuttings with white on the bottom do seem to root a lot quicker.
This answers Vinny's question: "The removal of old, exhausted soil from the stools and the substitution of a rooting medium... has a considerable influence on the number and quality of the cuttings produced. Casual treatment at this stage may well be reflected in second-rate results throughout the season..."
Having said that, see this picture:
I guess there was more than one way to do things, even back then!