Some other things I thought of that could make your CV stand out / improve it - you could put links to preprints of any papers that are more or less ready to be submitted. Then they can at least read them. Or you could preregister any studies you haven't yet finished analysing or writing up and put them as sort of protocols on osf (it's free and respected / widely used) . These can go in a publication list.

Earlier you mentioned about assistant jobs only requiring a bsc or masters - that's OK, you can still apply, especially if you haven't yet been awarded the PhD. Many people do this.

I'll post if anything else comes to mind!