René, it looks like your pen is a 'Bailey Light.' I found a blog where someone is comparing the old Bailey and the Bailey Light. This person states the new Bailey Light will accept the threaded converter as well as the non-threaded converter and shows a photo with the push-on converter attached.
I don't have any Cross fountain pens, but my experience with converters in general is there can be slight inconsistencies from one converter to another. I've had a situation where two seemingly identical converters won't necessarily fit the same pen. Maybe your particular threaded converter is just slightly off enough to not fit.
Here's a link to the blog I found: https://rupertarzeian.com/2019/10/19/early-thoughts-on-the-cross-baile
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