[amelia] Including all my analysis FEs

Hi All, I'm working with panel data (state-years) and a difference-in-difference design. I'm looking to fill some values in the dependent variable time series. My main specification is thus just two-way fixed effects (state FEs and year FEs) and a treatment variable. I've gotten the best results modeling the missing data by running a local polynomial regression (a la Honaker and King 2010) for each state, and then using those predicted values as the predictor in Amelia. (i.e. run I run a local polynomial of my DV against time for state S, fill those values in to my predictor variable for state S, repeat for all states) Everything I've read says I should definitely include all variables I plan to use in my analysis in Amelia, but I worry about failing to meet multi-variate normality conditions with the FEs, and running the model with and without them, I'm not sure they're adding much. Do I *need* to include all those FEs (i.e. will I introduce some weird bias in my subsequent analysis if I don't)? And if I do, is there anything I can do to deal with them definitely not being multi-variate normal (or do I not need to worry about that)? Thanks! Nick