To my mind (FWTW ) the main problem with VHL (Very Heavy Lift) LTA transports is the weather and atmospheric conditions. I have no real idea what speed a modern LTA heavy lift vehicle could travel at in still air, but it would have to be able to avoid heavy weather - by flying around or over(under?) even moderately serious heavy weather. In theory there would be a practical limit in altitude (based on the structure and payload vs the gross lift of the gas envelope volume) above which the heavy lifter could not ascend. I do not know enough about the structural weights and such to give any numbers.
Those of you more familiar with the civil and military aviation industry can maybe answer these questions:
What would be the max altitude needed to get above heavy weather to about the same degree as airliners?
And how often would this be necessary for a trip that could be upto halfway (or more?) around the world?
Weather during landing and launch periods would also be a concern, as would handling and protection on the ground. Would it be practical on a VHL LTA vehicle of the size we are thinking of to recompress the helium while on the ground? That would create a HTA airframe when not in flying trim and might solve the potential weather effect problems while on the ground.