Space racing controls? 13 in one back pack, and 7 in the other
I carried 10 with room to spare in my granny basket. It made for very easy pickup.
Basket would be nice, easy to get to, but you need to keep the bike standing up, otherwise you cargo will fall out
as controls are usually attached to something that a bike can lean against, it wasn't a problem. And I didn't even need to dismount when picking them up - just lean over to unlock, and dump it in the back.