There is a fault in your question.
And I only just got to look at this question now.
edit: I wasn't thinking properly and made a mistake, I was confused with the conditions and I thought that the team couldn't play in some conditions but I see you resolved that in your question, so yes there is no mistake
Ok I'll try with this attempt, first name the conditions in the question, (1) and (2).
There then initiates four cases that we only observe for Defense (D) and Forwards (F)
It's possible to do this because your conditions don't make sense if they apply for people among different lines.
We will simply ignore all arrangements for goalies, I'll multiply my answer by arranging defence and forward by 2 at the end.
Case 1:
Case 2:
Case 3:
Case 4:
So my final answer is:
10808
Is it? It might be wrong because I'm quite weak with permutations and combinations.