I am trying to run a cloth simulation on a dynamic shirt that I have worked over with the morph tool.

When I run calculate the sim I get all sorts of odd things happen. I understand that there is a known bug in Poser (P10) that duplicates a morph, so setting the morph dial to zero helps to keep it from going berserk it still doesn't look like the sim is working as it should.

I've also tried exporting and importing the dynamic shirt but that's not working right either.

Does anybody have any tips on working with morphed clothes in the cloth room?

Can you be more specific.  Simply stating odd things doesn't give anyone much to work with.  Can you give a link to the skirt?  It could be a weld issue, it could be that you need to constrain groups.

Try morphing the prop with the morph brush and saving the morphed prop to props library under a new name.  Load the prop and check to make sure the prop doesn't have duplicate morphs.  If it does, you may have to open up the pp2 in good text editor and remove the duplicate morphs. 

If the prop doesn't have duplicates morphs and otherwise looks good, try running the sim on the new prop.