Can’t help on the maths (other than to say a lot!) but it seems the most logical way of launching something with such short notice - using solids that is rather than trying to invent orbital refuelling quickly.hopefully ignited sequentially.
How much G-load would a pair of SRB's generate on a vehicle like that?
Considering that each shuttle SRB weighed 590ton however I’m not sure what the launch campaign would look like. Maybe launched segment by segment and assembled in space near the ISS/using a shuttle and its arm.
Perhaps Enterprise would be cannibalised for the cockpit, you’d need the other orbiters going flat out to bring up materials and components. Maybe the cockpit would be launched unmanned on the side of a ET/SRB stack.
Probably worth exploring some of the abandoned plans for bringing things up in the STS ET - either in the aft cargo carrier position that was abandoned after Challenger or as a hammerhead fairing - with the proviso that lack of ability for RTLS was a risk you were willing to take.
Interesting thought experiment really.