I have a classic edge skuttle and find that the cln conk pucks, as well as the Edwin Jagger pucks sit well in the lid.
As far as which soaps I find lather really well in the skuttle itself, The above listed as well as Crabtree/Evelyn Work well if you work the moistened brush in the puck a good 30 seconds then move to the skuttle and add a little water to the brush as you mix, as required.
Creams such as Cyril Salter, Real Shaving Company, or Proraso applied about almond size again to the pre soaked brush than worked to foam in the skuttle bowl work awesome too.
My routine is close the sink drain, fill the sink and skuttle outer chamber at the same time with hot water but leave the mixing bowl dry ish, then I soak my brush in the spout of the skuttle a few minutes and use it to collect the soap from the puck or tube and transfer it to the skuttle which I then take out of the sink to use as I mix up the lather. Use the half full sink for blade rinse between strokes as I shave.
Hope some of this helps.
Cheers.