The building I live in was erected in the 1960's and doesn't have great service for Verizon or AT&T (I would know, I've been on contract with both). A bunch of dudes in the building I live in use AT&T and Verizon air cards pretty effectively. I've heard no complaints, but for now I'm sticking with Time Warner myself.

Ok now I understand what you're thinking.
I suppose you could take an MGRS coordinate and chop off the starting digits for a local area, i.e. your town/city falls entirely within the RT56 100 km^2 grid square you could tell everyone working in the area that RT56 is assumed and that 777888 will be understood as RT57776888.
The problem I can see with this approach is your in-house software and familiar reporting techniques will be alien to state and federal forces that may be called in during a disaster such as a hurricane, large riot, CBRNE event (Chemical, Biological, Radiological, Nuclear, and High-yield Explosive), etc.
I agree that latitudes and longitudes are difficult to use, and that's why they came up with MGRS. All my professional experience with land navigation and GPS is with MGRS and it really is an easy system to learn and use.

The grid-based system you're thinking of has already been implemented for years as UTM, MGRS, and new USNG.

MGRS is used in many technologies familiar to ground troops, such as the PLGR, DAGR, and BFT.

MGRS is used for land-navigation, as described in the Armys FM 3-25.26.

MGRS coordinates are regularly used in common radio traffic, such as the MEDEVAC request, UXO/IED spot report, and call for fire.

Many consumer GPS devices support MGRS.

Hey, everyone has a right to mangle a sill-ah-bull now and then.

I've had a lot of women complement me on my Toyota Tundra, and I always answer "I have a lot to compensate for." Always makes them blush.

I'll throw this out there as a Soldier recently returned from Iraq: everything gets ruined by the sand. Everything. The CD drive in my computer doesn't read most store-bought DVD's and will not burn anything. Sand got into the lens on my camera and scratched the glass when the shutter closed. My buddies work computer over there made a disturbing squeak anytime the fan turned. Another friend zapped an Xbox with the 250VDC they use over there (yeah, that one was avoidable). We had to replace all the laptop batteries for one of our Forward Surgical Teams after the heat ruined their ability to keep charge. Bottom line: commercial electronics don't fare well in Iraq. The sand isn't like American sand - it's almost as fine as flour, not rough like sugar crystals. I haven't been to Afghanistan so I wouldn't know if it's better there but I wouldn't take anything expensive. Another idea I'll throw out there - see what you can do for making a transformer that will work with the HMMWV's 24VDC batteries. That's something he could share with everyone in the vehicle and it'd be fun, especially as a DIY project.

Those rechargeable batteries aren't quite as reliable as people will tell you and they're heavier than the single use batteries, although in theory you won't need to take as many to the field if you have a way to recharge them (generator, solar panel). Also the single use battery is considered HAZMAT even when discharged as it may, may, explode upon contacting water so you can't just throw them out once they're used.
In the light infantry medics and RTOs end up carrying a lot of stuff (not to say the poor dude carrying a mortar tube has it easy). I sure hope this project works, soldiers and marines have a very heavy burden to carry once you add communications gear to the body armor, water, weapon, ammo, rain gear, etc. You get used to it after a while, but with stealth and mobility being the direction of modern close-quarters urban combat changes need to be made.
Cutting the weight of communications gear isn't the only way to make the modern warfighter lighter. The future may hold caseless ammo, lightweight and flexible armor, and maybe a better weapon (not saying the M-16/M-4 aren't great, but it gets heavy after carrying it all day).