I have a couple of suggestions... but you've likely considered them.
As you said... more work to implement.
Assuming you'll allow additional party members to join in on recruitment missions:
1. If the party is full, then when a recruitment mission is triggered, bring up a screen to prompt who to drop. After the mission, the team consists of the team that just played the recruitment mission.
2. As above, but the existing team is flagged and after the mission the original team is re-assembled, minus the new recruit.
If only the main character goes on recruitment missions (as it's currently implemented):
1. At mission end, bring the player back into the Team screen so they can re-add.
2. Put a flag on the current team members and then re-add the existing team back. If there was already a full team, then the newest member is not added. If the team is not full, then (as they are currently) they are flagged as being in the team.
3. After a recruitment mission, bring up a message telling the player to go to the Team screen to select which characters are in the new team. (This would be the simplest solution)