I want to say you should be able to treat perilla like basil seeds, but I actually don't think I've ever needed to intentionally sow those seeds.
They reseed like weeds in my garden, both green and red, and pop up in my indoor containers as volunteers. I'm not even sure if I saved any seeds.
They are drought tolerant but do well in heavy clay. My garden tends on the acid side, but perilla adapted to your garden may be completely different from ones that have been growing in my garden for years.
I've never used 100% perlite as seed starting medium -- are you going to grow hydroponically? My seed starting mixes are usually 1/3-1/4 roughly screened compost, 1/4-1/3 sand, and 1/3-1/4 topsoil (yeah, yeah, they don't add up), or 2/3 commercial premium potting mix and 1/3 sand.