I'd tried to find some pictures of the J35 online to see how the carrier fits into the head, but no luck.

I did find this advertisement for the J35 from 1969:

I also think you should use this enlarger at least to learn the basics. For now I'd even clip a single negative frame so you can at least try out the enlarger. The issue about how to fit a 35mm strip into the carrier may need more photos showing how the carrier fits into the head before it can be solved.