I think the earlier you remove those holes the better for the wasps. Alternatively the holes should be empty some time in the spring.

These wasps will not stop filling holes and the last brood of the year will only hatch in the spring. After which female wasps will shortly start to fill the holes again, so there is never really a “good” time to do it. Spring after hatching would do the least damage. But there certainly is a “bad” time": You do not want to destroy the last brood of the year, that would more strongly impact the population than doing it while the female is still alive and can lay eggs in other holes.

Btw. that Insect Hotel is doing nothing for those wasps, because it will only house bees and wasps that lay their eggs into woody material. If you want to create a place where your specific parasitic wasps can flourish you need to have a hotel with dried clay with holes in it or even fired clay with holes. Because those species specialize in laying into specific materials.

Btw. remember to brush out all the holes or renew the papyrus-pipes in spring.

I don’t know if it would be possible, but maybe tape small paper flaps over the holes? That way, anything inside could get out as the flap would open easily that way, but getting in would be much harder.

Whatever you do, don’t seal wasps in. They will make their own exit if none exists.

When would it be the best time of the season to seal them off?

I doubt the holes are big enough for wasps, maybe not even for bees. But if so: Bees are likely to stay, wasps might move on in autumn (?) So, without harm, it depends on who came to live there but maybe without harm isn’t an option. You could wait until it seems abandoned and fill the holes then.