I'd be interested in how to propagate Fatsia Japonica and keep it from wilting in this heat.

I have successfully rooted cuttings.

They are slow, but I used the standard procedure of a bottle of water in the kitchen window sill.

I did it in the spring before the new stem was hardened.

I also tried woody stem and root hormone but was less successful with that. Some took but others didn't. If I recall correctly I got 100% with the rooting in water method.

Good luck.

Established plants will sucker; dig and re-pot the suckers.

Cuttings have been very easy in my hands. Make sure you get a piece of trunk or stem, or a heel. If the leaves are big, I trim them up to reduce transpiration. I dip in rooting hormone powder, and place in 1:1 peat:perlite, and keep moist and shaded. No humidity domes, no bottom heat.