I made a few batches of triple cream Camembert, glad to share my observations...
no stirring obviously but ladling the very soft curd into the butter muslin is the norm... Trick is to get a "perfect" piece of butter muslin... One that drains quick enough and without loosing curd. I find they come in various qualities and drain characteristics. Some Butter muslin are too tight of a weave ..once you find a good one ..buy lots and keep it handy just for This type of fine drainage. Drain by hanging and slowly twist the bag and rest on side of pot (used to catch the draining whey) so as to not untwist, aiding the long draining process.
I recommend: Leave curds in molds a long time ... The extra soft cheese will have a tendency to have elephant feet fresh out of the mold...sagging and barrel squatting .. Just flip them often often.
Good luck....hope this helps with your cheese type.