How to make homemade ice cream with a chocolate swirl
When I've done this in the past, I did two things differently.


I used more of a fudge sauce that would thicken and get somewhat firmer when cold.  Like a fudge sauce or such.  Syrup just mixes too easy.
Mixing a swirl into a deeper container like the churning tub proved somewhat diffcult.  As I tried to swirl, it would mix instead.  Instead, I spread the ice cream in a large cake pan, poured the fudge over, swirled in a bit with the knife and then set it in the freezer for about 1 hour.  Then when everything was pretty firm, I scooped it up into the final container in as large of sections as possible.  It worked great.