I hadn't heard that Perilla / Beefsteak Plant needs cold moist stratification. Tom Clothier says:
Perilla frutescens , beefsteak plant , Ocimum frutescens, P. ocymoides,
Type= an , , sow in light @ 70ºF , 15-30d
So they might take 2-4 weeks just to germinate. But I think the plants like hot weather.
These ATP Plant Database entries had some comments that mention Perilla reseeding aggressively:
Shiso (Perilla frutescens)
Beefsteak Plant (Perilla frutescens var. frutescens)
It wouldn't surprise me if they were short-lived seeds, and I didn't store these with desiccant. And they are getting on in age. But on the bright side, I ran out of most varieties some years ago, so maybe only the less-old ones are still kicking around.
I'll look tonight and see what I have left.