If you don't have the time to fight 15 minutes per AQ, just do a lower one and AAB it?You should do what you find more fun. Without a couple of Miracle Tickets, your Light team isn't exactly glorious either - though it is decent.When it comes to sharing to "All" I don't think Ranks matter anymore. It's just a matter of luck. I keep opening my Ult farm to All and even get Rank15s to leech at times (which is exactly why I open them - it's not like I need help).
Anyway, your best way to find more Raids is to have an active Friend list. If you have lots of Friends sharing lots of Raids, then well... you'll see lots of Raids. Also, an active Union REALLY helps too.Never +99 any Hime.
Think of it this way: You can either give +3 Atk +1 HP to ONE Hime in your team... or you can give +3 Atk +1 HP to ALL your Hime if you put that +1 to a weapon in your Grid instead. It's quite the no-brainer. You'll never get to +99 any of your Hime because of this, really.