Ok, quite the post. I'll try and help you out as best as I can here.
First things first. I think you need reconsider your electrical needs.
Let's start with the inverter. You are looking at a MASSIVE inverter.
Watts are watts. If you have 5000 watts on the AC side, you need 5000 watts on the DC side.
Watts=volts * amps
So...5000 watts on the AC side means you have 41.6 amps available
Now lets calculate the DC side of things.
5000/12=416.6 amps (!!!)
Your inverter won't often be at full load I don't think, but we're going to plan on 415 amps since it's close and a nice number.
Now let's look at batteries. The 120 minutes to 10.5 volts you were referring to is called reserve capacity. It is one of the ways of expressing the storage ability of a battery. It is calculated by taking a battery at 80* F and putting it under a 25 amp load. The number of minutes it can maintain that load down to a voltage of 10.5 volts is the reserve capacity. I hate using reserve capacity. It is complicated and no more accurate than amp hours.
Amp hours are just that...amps times hours. 1 amp for 5 hours is 5 amp hours. 5 amps for 1 hour is 5 amp hours. In reality they aren't equal, but more on that later.
A GC2 sized 6 volt golf cart battery is going to have about 225 amp hours of capacity. Since it is 6 volts you will need two of them wired in series to 12 volts, but this will not increase your capacity. You will still have 225 amp hours of capacity. Easy enough, right?
Well let's look back at your inverter load. It was 416.6 amps at full load and we're just going to call it 415 cause I like whole numbers.
So we have 225 amp hours available to us. We are drawing 415 amps. 225AH/415 amps=.54 hours of run time on a pair of golf cart batteries.
Oh but it gets worse...This little German fellow named Peukert determined that the higher the rate we discharge a battery at the lower it's amp hour capacity will be. Remember the 1 amp for 5 hours versus 5 amps for 1 hour? Both are 5 amp hours, but because you are discharging the battery more quickly in the second example you will actually need a higher capacity battery. You might often see golf cart batteries labeled with their reserve capacity at 25 amps (the standard) and at 75 amps. Thanks to Peukert the reserve capacity at 75 amps is less than 1/3 of that at 25 amps. Your 415 amp load is NOT going to last for half an hour like the simplistic equation of amp hours divided by amps would lead us to believe.
Thought it couldn't get any worse? Oh it does! All those ratings are to a battery voltage of 10.5 volts. A fully charged 12 volt battery is 12.6 volts (2.1 volts per cell). Fully discharged it is at 11.8 volts. Clearly 10.5 volts is far less than "fully discharged." To add insult to injury a deep cycle battery should NOT be discharged to less than 50% of capacity for the sake of lifespan. More than 50% discharge and you're doing permanent damage to the battery, deep cycle or not.
So...we don't want to draw our batteries down to less than 12.4 volts. That means our 225 amp hour pair of golf cart batteries really has only about 100 honest amp hours to give us. Ignoring our buddy Peukert for a minute that is going to only give you about 15 minutes of run time at full inverter load.
Pretty depressing, huh? Never fear. 12 volt living IS managable. The first and easiest solution is to just add more batteries. But there are limits as to what our pocketbooks can take and how much space we really want to lose. On top of that you are limited as to how fast you can recharge batteries. Remember our 15 minutes of run time? Well the general rule for recharging batteries is to keep the amperage at or below 25% of the amp hour capacity of the batteries. Since we have 225 amp hours we should keep our charge rate right around 50 amps max. Since we took out 100 amp hours we need to put 100 amp hours back in them. 100 amp hours divided by 50 amps=2 hours. Yep, we need to recharge those batteries for 2 hours after our 15 minute drain period.
So what's the next solution? Well, reduce the electrical load! Don't run the microwave unless the bus motor is running (alternator power) or you are plugged in. Try not to use the AC unless you have alternator power or shorepower available. Your wife's beauty stuff you were worried about? Look into camping versions. I have seen blow dryers and curling irons that ran on butane. Or just use a towel to dry the hair and rollers to curl it if she must do those things at all. Heat your coffee water with a propane stove and use those teabag style coffee pouches. It really is easy to do!
I don't mean to take the wind out of your sails. I just want your system to work well for you. It's best to plan realistically and then be surprised later at just how well it works.
If you're looking for more reading on the subject I suggest the poop sheets. http://www.phrannie.org/phredex.html
Oh yeah...as for the electric motor driving an alternator...you were right about no such thing as a perpetual motion machine. If the alternator produced 1200 watts (100 amps, 12 volts) the electric motor will inevitably require 1500 watts to turn it. It's just the way it is. You could, however, drive that alternator with a small gasoline engine.
I hope this helps.