Can you point me to the specifics of the federal statutes that make this illegal....at least for now?
All aircraft, manned or unmanned, need an airworthiness certificate from the FAA to fly in US airspace unless the FAA exempts them. The FAA regulations exclude "models" from this requirement. There's an FAA notice that seems to say that a "model" has to be flown lower than 400 feet and within the operator's line of sight to fall within the exclusion. I say "seems to say" because it's more an illustration than a definition. (All this is from memory, so details may be off.) The FAA has occasionally given permission for a particular UAV to be flown (I think it was for a police department or some such).
Now, an FAA "notice" isn't a statute, and it's possible, I suppose, that operating a UAV beyond line of sight might be held to fall within the exception for "models," especially if it doesn't go over 400 feet up, which it normally wouldn't. Personally, I wouldn't count on it, and I wouldn't want to foot the bills for the legal fees, either.
One more thing worth mentioning, maybe. Lots of people (besides the military, which is exempt) are interested in developing and/or using UAVs for things like police work, crop dusting, and patrolling borders. I believe the FAA is studying this area and it's surely only a matter of time until some new regime for regulating UAVs gets set up; they're just too useful to ban. The whole matter ought to be clarified then. Let's hope modeling doesn't get shafted in the process.