Oof, I tried like twenty different statsmodels methods and finally got what I want although I honestly don't really understand from the docs why this works and .predict or .forecast don't.

I finally got what I wanted using .apply(). For my data:

fore=model_fit.apply(endog=oos_df[outcome],exog=oos_df[[exog vars]])

And then I can retrieve the values using:

print(fore.fittedvalues)

Hope this helps someone who is wondering the same thing!