Personally I loved Zagreb when I was there. I just spent ages walking around the old town and enjoying some of the restaurants. I visited the Museum of Broken Relationships (yes, that really is a thing) because it was just something different. The place was irritating but not impossible to cycle out of.
I can't answer the question on your specific border crossing because I crossed into Slovenia on the coast somewhere near Piran. FWIW, I didn't have any problems at all there.
Do you absolutely have to take the direct route from Zagreb to Ljubljana? You'll miss some pretty amazing places by going direct.
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I am clinically insane. I am proud of it.
That is all.