Before I start, let me say I ask this just out of pure practical considerations. I understand the story considerations and all. So what stops the knights from going away after their 40-days of service (or is it 60 days)? Do we assume Earl Roderick pays their stay out of his own pocked? What about Arthur? How does he get his lords to stay after their 40-day service pledge? The Battle of Carlion is around May, 10th, then the Battle of Bedgraine is in July, and the Battle of Carohaise in August. Yes, there's that thing called Loyalty (Lord) but still...

Also, it states that all knights receive £20 in silver from the roman treasure (£40 if you participate in the adventure). Is that £20 for the barons and earls or £20 for EVERY KNIGHT in the army?

I think you just answered your own question.

The knights are grumbling about the extended service, and Arthur rewards them ALL with £20 each. I'd limit that to vassal knights, though, and give the Barons like £10 per household knight, and let them gift their household knights from that.

The 40 days of service is the number of days which are required to be given for free. After that, the Liege has to pick up the tab.

The 40 days of service is the number of days which are required to be given for free. After that, the Liege has to pick up the tab.

Hence my initial question.

Hence my initial question.

Note, however, that the knights & barons can VOLUNTEER to serve for longer out of their own pocket, too. This is what I expect has been happening. After all, if Arthur goes down, all those Eager Vassals will be left holding the short end of the stick with High King Lot. Since about 80% are household knights sworn to the barons, even if individual vassal knights would peel off, it is not a great loss to the army. However, this would give a very nice story opportunity to underline the difference between the Eager, Good and Reluctant Vassals, by having the latter grumbling about the extended service around the time of the Battle of Bedegraine and threaten to go home, only to be kept in line by a promise of a reward by Arthur.

Also...

The Battle of Carlion is not planned by Arthur. It is his election as the High King and a celebration that the northern kings interrupt. The knights are there to witness this event and party, and are suddenly pressed to service to defend their lieges. If you have the actual muster of troops in mid-to-late May, you can have the Reluctant Vassals grumbling just before the Battle of Bedegraine in early July.

As for the Battle of Carohaise, see how small Arthur's army is there: mere 600 knights. He could probably support that number of knights just by himself and his Eager Vassals.