It is recommended that you cast it in halves (left & right). If you are casting a rocket, cast the
feed, burn tunnel, and possibly a short section of the heat riser in a left and right half configuration. Assemble it with a ceramic paper gasket between the two pieces and it is all held together with stainless banding in a few spots. The riser can be poured in one piece or poured in short sections of tube and mortored together.
You can buy lightweight refractory mix that does not require perlite to be added. You can use the perlite around the cast core for insulation without modifying the mix. The place that I bought my castable mix from did not recommend adding anything to the mix.
Also in consideration,
Dragon Heaters cast their rocket cores in a single piece.
I could not find any documentation about the ks4v so I will not comment on that.
Good luck with the build!