Is there a reason you wanted the lees from the rum wash in the still? I would think you'd want to leave that in the container to prevent any off-flavors.
if you get it already made, that means it's only hearts. this is the same way that distilleries source their vodka for gin. It's already done, no need to sit there making cuts.
Great video, I’m a little confused on the cuts with the gin, the heads tends to have a lot of heavy oils in and and you distilled right into the tails unless I missed something this usually makes the gin loosh and gives a off taste in the gin