While I'm at it and back on my soapbox,
I get where you are coming from. I've been an amateur radio operator since the late 80's or early 90's, and the amateur radio attitude you speak of gets annoying really quickly. I work in the communications industry, and have for 25 years, and sometimes it gets pretty funny when the amateurs start up their antics.
Enough on that, but I hear what you are saying. Amateur radio is not what you are looking for.
But, lets look at FRS too. Those $10 FRS/GMRS radios you speak of are very poor performers. The actual output on these radios is often far below the claimed wattage. It's not uncommon to see FRS channels running around 300mw, or 60% of what is actually permitted. Add in the inefficient antennas and the range can be pretty dismal.
A store and forward repeater like you are talking about will be a major headache. Trust me. If you are expecting a bunch of people that just spent $10 on their Wal*Mart radio to figure out how to communicate through one, you are going to be disappointed.
First off, someone is going to start talking. Someone nearby is going to answer while the store and forward repeater is trying to do it's thing. Some guy a mile away is going to hear a bunch of garbage. Someone is going to complain because they have to hear everything twice. Batteries are going to run down quickly because it's going to be running at a pretty high duty cycle. It's going to be a mess.
Also, expecting much range out of a store and forward repeater using 500mw, or even 5 watts isn't going to go well. 5 watts might get you what you need, but what you really need is altitude. Getting the whole thing up high on a hill, pole, whatever, is going to do more for your coverage than anything else.
What I think you are looking at here is a cheap radio and wanting it to perform like something much more than what it is. Sure, there are ways to do it, but you'll run up against user issues, cheap equipment, etc. Legality issues will be there, too.
So, the legality issues don't bother you? That's OK, that's your decision. But, if you are going to ignore the rules, then why limit yourself to a $10 FRS/GMRS radio? You could certainly do better with a higher end radio/antenna system as your store and forward system.
However, remember, you are going to have a bunch of random people with a $10 radio they just picked up at the store. Expecting them to actually read the directions, get it on the right channel (FRS/GMRS channels are not always number the same between brands), as well as figuring out the PL/DPL tones "interference eliminator codes", call tones, etc. it's going to turn into a mess really quickly. Add in the confusing nature of a store and forward repeater, and hilarity will ensue. I actually really enjoy hearing a recording of how this worked out. I bet it would be a real hoot!
Call tones through a store and forward repeater are going to cause you to pull all your hair out.
I personally think you are making this way to complicated. CB radios will do what you want. While they are not $10, you can get a decent one for $50 and a mag mount antenna for a bit more. You can get them at Wal*Mart, too. It'll have the range you are likely looking for, and they are a lot easier for unexperienced users to operate. No PL/DPL, just set the channel and talk.
Trying to make a $10 toy do what you want is going to be an exercise in frustration. You are certainly welcome to try it, but I think you can do better.