This is a job so seldom nowadays that I had difficulties finding the English translation in the two online dictionaries I normally use for a first glance: be a Reisemarschall.
A bit of googling brought me to terms like “coordinator of the papal trips” (which would be correctly describing Mr. Gaspari’s position as “Päpstlicher Reisemarschall”, of course, but would be too specific as a general term, even if he may be the only Reisemarschall left – yet “coordinator of the [enter head of state’s title] may be an option, although not sounding as traditional as the German term “Reisemarschall”) or “Papal traveling coordinator” (the latter link showing you can even get a decoration for doing your job from the King of Spain and giving the option of “traveling coordinator” as a general job title).