Welcome to the community.
First and foremost the subject here is asana. When the other tools of the practice are extracted (like homogenized milk), we can’t logically call it “yoga”.
Your post, to me, begs the following question…If you’ve found something that truly works for you then why the continued hunt for something? But perhaps this will just remain a rhetorical question, for now.
No sound asana practice is [I]only[/I] about flexibility/mobility. In order to be sound (read: safe) the practice must include stability as well. Otherwise it is merely contortionism and you can catch on with Cirque du Soleil.
Generally speaking, it is not so much the type of yoga but that approach, intention, actions, and commitment of the student.
I work with several athletes and I merely construct something based on their needs, overtly expressed and otherwise. Find a good teach with a practice that can and is modified and varied (rather than static or “the same”) and you’re athletics will be served. Or you can work with me:-)