Perhaps just faster travel. Afterall, it is just a noble and a small honour guard that is traveling, they should be able to travel much faster than the troops.
If this is already the case, just increase the speed.
In any case, the hunts would only be local so would not require the travel times. I would think that hunts should only last for two or at most three days.
Also, I have completely disregarded the single hunt idea. If that is the part that people are interested in and want to develop, then I have lost interest and would not use the feature.
Increasing the food does not make much sense, perhaps a bunch of people are fed for that feast, but they are over eating and are not the lowly peasants.
