The thing I find difficult with FAKs is that you really need to have a good idea of what you are going to use it for. For urban areas if you might be helping a stranger, then gloves are critical. gloved hands hold a major injury nearly as well as anything, and you can probably have backup within a few minutes. beyond that everything is for your own comfort. I'm not a fan of back pockets for anything, but that's me.
Get non-stick gauze, and you can use it to add to the padding under bandaids, or use the bandaids to tape it down. Alcohol wipes are pointless, you shouldn't use them on wounds, and if you are doing surgery on yourself, use a lighter. Polisporin is up to you, but for a back pocket, I think the little packets won't stand up to the abuse.
First aid stuff is a great idea. How much or how little is going to depend a lot on where you are. Personally I think if you are going to back pocket carry, you won't get much more than a pair or two of gloves, and some bandaids and a couple thin non-stick gauze. But if you are balancing out a fat wallet in the other pocket, you can do even more.
The main components of my EDC dooom-bag first aid kit are:
gloves (2-3 pair)
steristrips
non-stick gauze 4-5 1.5x2 or 2x2.5
assorted bandaids
2 packets emergency dehydration salts (hydrolite at the moment)
2 roll gauze, (packing or compression for larger wounds)
assorted thick sterile gauze
rolled elastic bandage (sprains and snakebite)
This (apart from the gloves and rollers) fits in a small ALOk sak ends up about half an inch thick. That covers me for pretty much anything that I will reasonably run into, anything beyond that is an EMS call anyway. I carry a bunch of stuff just so I don't have to re-stock every time I pull out a bandaid.
I'm not trying to trash your plan, but I've watched people try to bandage up an injury with a very small FAK and half of it was useless since it was very injury specific, and the the other half was not enough to cover the wound. And the wound was such that the person could have probably walked it off anyway.