Wreckerman893 that is wicked insight, you rock! Have you worked a lot with these types of truck specifically?
I was in three different military units that had the A2 5 tons. There are a lot of nuances and tricks of the trade that you pick up.
One is the electric fuel shutoff solenoid on the 8.3 Cummins diesel. They have a tendency to de-energize and will not open if the battery switch is turned on. This happens most often when the batteries are weak. This causes (an uninformed operator) to continue to crank the engine causing wear on the starter and further draining the batteries. This requires you to either have a "Soldier B" to hold it open or to zip tie it open to get the engine to start.
You can also shift the big Allison transmissions without hurting them. Unless they have been set right at the factory they will upshift too soon and you will lose power when in a hard pull. I recently flat towed an M818 while carrying another M818 on the back of my M927A2. I upshifted and downshifted to take advantage of the power band and the braking effort.
Due to the automatic transmission you cannot pull or push start these trucks. If the batteries are dead you either have to slave the dead one off (using the slave ports on both trucks and the military issue slave cables) or you have to jump them with heavy cables using two twelve volt batteries set up to produce 24 volts.
Having the batteries under the passenger seat makes working on them a real pain in the arse, especially if you have to replace them.
One redeeming feature they have is the tilt up hood. It makes servicing and working on systems a lot easier but you still have to do a lot of climbing on the trucks with the super singles. I really hated working on the 800 series and having to stand on my head to do stuff in the engine bay. Get a small step ladder and take it with you everywhere.
A note here about military fuel gauges: They have never made one that is reliable. The only thing that lies more convincingly than a career politician is a military vehicle fuel gauge. I never, ever let mine drop below a quarter of a tank. If you are going to do a lot of road driving I'd invest in at least two 5 gallon containers to carry full at all times. You might even consider installing another tank on the other side and a fuel transfer pump (you do not want to mess with the factory switching system that comes on the wreckers, tractors and dumps, trust me on this one). That would give you a lot more range and a good margin for error but again you do not want to run the system dry.
There are upgrades that make these beasts a little more user friendly. Moving the batteries out of the cab and installing air ride seats and air conditioning are recommended if you plan to drive a lot. You will absolutely cook in one of these trucks in hot weather. Hot and humid weather is ever worse. My eyeballs have sweated driving a M932 in the Korean summer heat. You can prob figure out a way to upgrade the mirrors to heated ones and improve the defroster (the 900 series were miles ahead of the 800 series but still marginal at best).
The long wheelbase and weight of the M934 will give you a lot better ride than the cargo trucks and shorter wheelbase trucks and the super singles ride better than the duals. But that also creates a problem with the turning radius.....my truck takes a big area to turn around in. You have to swing wide on most turns especially on two lane roads where there are curbs at the intersections. Swinging wide will often put you into oncoming traffic and can be unnerving to those approaching you in that lane. Always be courteous to the other guy and don't bully your way into traffic if it all necessary. We try to put forth a positive image. I cut clueless people a lot more slack in my truck than I do in my little van.
You will attract a lot of attention wherever you go. Most of it will be good but occasionally you'll meet the odd A-hole that doesn't like (a) the military (you are guilty by association with these types) (b) big green trucks that burn diesel fuel (I never figured this one out since trucks deliver virtually everything they use). (c) People that don't think civilians should own "weapons of war" and be able to use them for whatever reason (I usually try to explain that we are getting our tax money back but some people would cry if you hung them with a new rope so go figure).
You seem to be doing your due diligence here so hopefully you can make an informed decision and get something that suits your needs and wants.
Good luck in this adventure.