I want to preface this by saying I am NOT trying to be mean or trying to stop you from creating your fan fiction... but considering the reason you stated that this post exists, I figure I should lay out some things you need to know and things to expect when doing a project like this.
Basically: Considering your fan fiction takes place outside of the standard timeline, you can practically do whatever you want with any of the characters. They could have had time to change or mellow out, as it were.
Of course this can lead to the problems with fandom not critiquing or offering opinions etc... because this means there is little interest in the topic or concept that you are using said characters in. Writing a Fan Fiction that uses official characters is always the harder option if you want other fans of the series to like it. If you take a character too far away from what they are in the main plot, it's really no longer that "character" and is just your own character that maybe walks and talks similar to the original.
So certainly, if you are writing it absolutely for yourself, great. Go right ahead and enjoy. But hoping/expecting people to comment on a subject that they aren't interested in, despite some of it being from their particular fandom isn't always a guarantee... Especially when the other fandoms involved are either completely different from this one. This is why my favorite Guyver crossover is the really Old Bubblegum Crisis crossover; Heart of the Beast (and it's unfinished sequel, Soul of the Beast. BGC and Guyver have similar DNA and fit together pretty easily (both antagonists are evil corporations, just one uses biological creatures and the other mechanical. Main protagonists are a small group in powered suits etc...).
This is something we've had to deal with a lot in our own stories... If you can't keep the essence of the characters, you might as well just create new ones for you to use. This is a big reason why the Warrior Guyver fan fiction original characters are the main characters of our stories. Yes, it is set in a modified Guyver universe, and we do use the originals in ours, but we try and keep them grounded in the reality of the original story as much as possible ( like Agito secretly creating his own Warrior Gigantic... We did that back in 2000... Over 10 years before he secretly made his own Gigantic in the manga. Still a jerk!)
So, if you go ahead and make your story ( and you should. the more writing you do, the better you get at it), try not to be disappointed when people don't seem to want to read it. It's clearly not the kind of story they like, or they just don't like the crossover concepts. We have people that loath our stories, and that is perfectly fine. It doesn't stop us from working on them. So write your story the way you want. Post it in as many places where the fandoms you crossover with might like it. If you get hits and fans, fantastic. If not, it will be an experience to help you improve, or you can use your ideas and adapt it to something more original. Remember, even 50 Shades of Grey started as a Twilight fan fic.