Re. DOGA, the short answer is that a DOGA-sporkable fic has bad geography in it. The more of it and the worse it is, the better. It also has to be bad generally, of course.

The good answer is, here is an index of DOGA spin-offs (mostly hS's work). Read them and see what's worked before, and you'll have a much better idea of what will work now, plus how the department works in general.

Re. attempted murder... it's attempted murder. It doesn't matter what department they're in. What matters is whether it's comedic attempted murder or dramatic attempted murder (not recommended in this setting, please). We've got options ranging from the silly (e.g. literal chill pills) to the serious (being arrested, possibly remanded to the authorities in their home continuum or closest equivalent). But be cautious: if you try to write comedic attempted murder and it's not funny, then it may end up being trivialized attempted murder, which will not go over well at all.

~Neshomeh