Hehe, this takes me back to my earliest version of the Aurora Arcology. Used to be more like such rescue camps. Helping the wounded who survived the Sansha attacks in temporary hospitals set up in stations & secure containers.
Your suggestion of mobile depots is good however, something I wish we had back in the day, they make for nice & easy identifiable objects in space. Also, the icon is fitting (a bunch of mobile depots together are sometimes referred to as tent-cities/camps. Also, capable of storing alot & you can place m close to known risk gates. These are gates with higher chance of lootcontainers, either due to ganking, or because of goods that become illegal in the next jump (other empire/nation). The amarr border is great if you want to do civilian rescues as you'll bounce on slaves from time to time.
Also, outfit a dedicated rescue ship, agility & being able to jump into warp fast is important. Due to criminal counters, a covert cloak ship becomes a necessity if you plan to do it often. Got to approach wrecks/containers cloaked in known gank systems, but also ability to cloak & warp becomes important with criminal timers.
Storywise I know too little about the Blood Raiders to give you more detailed advise, but I think it would be a great way to spread the Blood Raider faith among a population if you do rescue work, also boosting Blood Raider rep among a population as you help their wounded & rescue people.
But perhaps it could be part of a Blood program? Visit hospitals in lowsec across the cluster (taking lowsec, as such regions would get less goverment assistance) offering them a Blood exchange program, they can order blood for transfusions from you, if in exchange you are allowed to run blood donation centers in their neighbourhood. Lil note, there's a Blood Fund item ingame, and it's tied to Bloodraiders! Found a link:
Blood Fund