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I have also had some similar trouble, CURA just copes with it, Simplify3D needs it to be split into separate models but then prints fine.

Its a problem I've had and its been a matter of the software.

but I will freely admit that if I was better able to modify the model to make it printer friendly that challenge wouldn't be one for you or anyone to face.

so, sorry for my part in it, and best of luck ^^