Before getting into my thoughts on potential options for the carrier plane itself, I wanted to mention a few nice-to-have options for the carrier plane itself. I don’t know that any of these is strictly required, but all potentially help:
For many reasons cryogenic propellants would be the best option for truly competitive air-launch. But both for boiloff reasons, and for providing cross-fed propellants during the gamma-maneuver, having some smaller propellant tanks on the aircraft itself could be useful. These tanks could be insulated more thoroughly than flight tanks, since the carrier plane is the least weight-sensitive part of the system.
One clever option that Doug Jones mentioned to me at Space Access if you have such tanks is to fly up to 30kft, vent the launch vehicle propellant tanks (one at a time)1, let the tank vent until it is at the now much lower ambient pressure, and then refill the tank till nearly full. Cryo propellants will boil at a colder temperature at altitude, and the heat absorbed by boiling off some of the propellants will chill the remaining propellant to this lower temperature, densifying it2, and significantly reducing the pressure needed in the tanks to ...