Itd be more expensive up front but if it were me, and I felt like running on genset power was going to be a common/semi-common occurrence with this contractor and others, given your tool load I would buy two small inverter generators like the Honda EU2000 or Generac equivalent.
First off, cordless tool chargers perform horribly on conventional square wave generators so the true sine wave power you will get from an inverted genset will make sure all your tools run at spec. Second, having these gensets means that they automatically idle down to deliver only the power needed. So for instance while your guys are fitting work and the only things running are the cordless chargers, the honda will run basically at idle and be almost silent and consume nothing for fuel. When you pull the trigger on a bigger tool, the genset will ramp up.
Having two of these means that you'd only have to run the second when your running the TS or need all 4000 watts. There is nothing worse than having a large genset whirring away, sucking down .75 gallons of fuel an our to power a light bulb or cordless charger.
If your contractor isnt compensating you with a higher number on your bid for not having his ducks in a row and power on at the job, fuel consumption will be a stinker.
Id be questioning why the GC is unwilling to have a temporary brought in (at his own cost) and deferring power demands onto the subs. Its one thing for a foundation or early framing crew to go without power but once your to the stage of installing cabs to not have power is, well, odd to say the least.