When a central TV deal is agreed it's usually a condition of competition membership that you move games (probably with limits on game numbers) if TV requests.
Entering the FA Cup carries the condition you must move any games requested by TV, starting with the First Round Proper.
However, I doubt any northern part time team will be too happy to travel south on a Monday, likewise us going north. Throw in the fact that Monday games could disuade London's more distant fans from buying / renewing season tickets and it might be worth the club raising the issue and letting fans know exactly what the rules they are subject too are.
As for Will, hopefully any Monday away games will be in his holidays or he's going to missing Monday away games. For many years the Post Office had a very good representative football team, many top non league players were postie's as the early knock off allowed them to travel to away games. These days a lot are self employed PT instructors, nutritionist and so on, again to permit easy time off work when required.
