I have a MEP 003A. I believe most of the military generators have three power configurations.
120V single phase
120/240 single phase
120/208 three phase
You "must" select 120/240 single phase if you are hooking it up to a house or panel box "bus" wired for single phase. There are only three setting for the power selector switch which is located close to the main lugs on the front side (or control panel side) of the generator. You can run in 3 phase mode and supply 240 volts to some motor or device if you put a step-up voltage transformer of the right size for the application device you are needing 240 volts to run. (e.g., standard AC unit, or 220V stove or water heater etc...) However, this can be expensive unless you find a used transformer that came out of some piece of control panel equipment. A new transformer that will handle 50 AMPs is expensive to buy. A Lincoln AC stick welder might work for this, but I haven't tried it yet. I'm not sure it is the right type of transformer on the output side. It's secondary winding is probably not big enough for a load of more than 10-15 amps. Honestly, I don't know... Anyway, if you're really in to it, you can google search delta - y conversions, experiments etc... It will take some electrician skill level to accomplish this modification properly. It's not hard, but you need the correct size of transformer to cover the load requirements, and... you cannot exceed 80% of the output current between the two 208 phases that supply the 208/240v single phase transformer which is going to be around 30+ amps on a MEP-003a generator.
I hope my information is clear and correct on this. If not, someone else can correct my "bads". I'm listening.
If you have a 803 I totally agree with your comment about how to set the phase switch. If you have anything larger than a 803 then there is no single phase option. Its 3 way (phase) or the highway.
Where I differ in your assessment is with the need for a transformer. If you look at the data plate on your AC it very likely says 208/230. Your dryer or any resistance based machine won't care in the least about 208v. The motors will care a little bit but they will simply pull more current to make up for it. That is unless the appliance motors are running off a hot-neutral split of the power supply and in that case they are happily getting the full voltage they are expecting.
Lets look at the AC unit. If you have a unit that pulls about 20a at 230v then it will pull say 22-25 amps at 208. That unit will be on a 30a circuit minimum so you are still under the 80% rule for breaker loading. You can't apply straight ohms law here because motors are inductors. The math gets a little more complicated but it can be calculated. There is a good chance the manufacturer has already done that and its on the data plate.
If in doubt look at the data plates for the appliances in question. In most cases there will be absolutely zero problem running single phase 240v equipment on 2 phases of 208.
Now back to unbalanced loading.. Why is it a problem to run unbalanced loading on a generator or 3 phase transformer? Coil heating? Nope. The electron gods will be unhappy?? nope. Its neutral current. You can burn the neutral in two if you have a high phase imbalance in a system (split phase or 3 phase). Specifically with these generators you can damage the Y bonding point with excess current. You're allowed by code to undersize the neutral. Something that in practice I never do.
How much of a threat is this in reality with these machines? In my opinion it is quite low but certainly not zero. From the practical side if you have a 804 for an ordinary house its much less if a problem than you think because how often is the energy demand in the house 10kw? Or even 8kw? I have to TRY to get the load that high at my house. Even if you do hit that level I doubt you'll sustain it for any length of time.
To add another layer here.. When you wire a 3 phase generator in a zig-zag pattern like what happens the the 802 and 803 machines its not a free lunch. You aren't making a 3 phase generator single phase. You are increasing circulating currents in the coils but the net sum of those currents equal split phase 120/240. You are creating a permanent hard wired imbalance between the coils that will cause more heat rise versus when you run it in 3 phase mode at the same power levels. BUT.. How many of us set our 803s to single phase then load them to the hilt? Anyone burn up an alternator? I've not heard of any. Anyway, its not the magnitude of problem that is commonly made out to be.
In a install where these generators were the prime source of power forever I'd put a lot more effort into balancing loads. Since they are used in standby service I would worry less about load balancing and more about keeping the mice out of them and the fuel clean. That stuff is much more likely to bite your rear end.