There is a Youtube video which shows a great way to make your own slug.
Take a fired case, melt a sinker into it using a propane torch (do it outdoors or in a well ventilated area).
Then knock the lead out with a kinetic bullet puller like the RCBS one.
You now have a dead soft slug that will not be a pain in the neck to drive into the barrel because it is too big. The taper from the bottom of the case should be enough to start the slug into the barrel and as you drive it, you will be left with only a tiny ring of lead that gets shaved off.
Be sure to lube the slug before you start driving it and it may be easier to cut part of the .38 special case down so that it is not so tall. The slug only needs to be maybe one-half to 3/4" long.