I'm casting a wide net here, but I was wondering if anyone here has had experience they'd like to share while running traditional FEA on piping components, and what troubles they came across trying to cross the boundary of beam analysis and 3-D/4-D analysis, while trying to meet the intent of a piping code.

Does the code expect the FEA user to extract stresses based on source? Sustained vs Thermal vs Occassional?

I think you can contact Mr. Tony Paulin, they develop PCLGold as a stress tool more linked to FEA.
There is a webinar available at
http://paulin.com/Library/Webinars/2011_...resWebinar.html

As a personal opinion, I think that a FEA analysis is well fitted with ASME VIII Div2 or ASME III but the Piping codes simplified too much the concepts, however remaining on the conservative side (that's why the improvements as Appendix P failed, isn't it?)