Too long, not reading the last three pages. I'm a new player, but would like to throw out a potential solution that I believe won't ruin the competitive nature of the Map Game while also providing the defense to not be overwhelmed IRL with the time they would need to put in to keep up with multiple invasions. But first, some context to this solution (which will be a second-hand account I received, to be clear):
Shadowbane was a highly competitive/hardcore PVP-oriented MMO where players could build cities on a map and other players could declare war, siege, steal, and so forth. Now the question this game struggled with was how to keep the game "fun" for players without bogging their base down with rules of what they can and cannot do, or else defeating the purpose. They isolated the experience they wanted players to have, and built around that instead of a concept. That experience is "PvP", the experience of fighting other players. The issue they were seeing was much like one we are seeing some people have, which is the OOC making the IC experience less fulfilling, AKA if cities were always siegable then enemy players would wait until a city's players were asleep and then destroy their stuff. Now, some cried fair play, that the city players simply did not commit enough, they should have had overnight watchers so such surprise sieges would not be possible. Now the city players could do that, but the devs saw the night sieges as a much more fundemental problem: by allowing it, it made the game not about PvP, but about avoiding PvP, finding times when players wouldn't be around to defend their stuff and destroying their stuff. In essence, it wasn't about whether it was fair or not, whether it was good sportsmanship or not, whether the other players should just step up or not. It was about the experience being delivered not the experience the game was meant to give.
So they made cities unattainable except during a siege window that is declared and known to both the attackers and defenders so that they could be on at the same time. Now, we have something similar, where you can't just take a hex, you have to declare the invasion. However, Shadowbane went further since this still allowed attackers to choose off-hours when they knew the defenders would be the weakest, again avoiding PvP. To counter this, they made a new system: Attackers would declare a siege, and the defenders would pick the time it starts within a given timeframe (choosing the hour of the siege within the week it was declared). Sure, the defender could pick a bad time for attackers, but in that same sense the attackers could choose a week that they're more flexible.
Now I feel we should also adopt this rule of "Defender's Right" where the Defender of an Invasion is the one allowed to choose the start time. As I'm told, Invasions last about 2 weeks, so the Defender could (for example) choose a time within a month, or four weeks. This way, should a faction be invaded by 3 other factions at once, the Defending Faction may spread out the invasions they're dealing with. They cannot postpone beyond the month (should they not declare a time within the month, the Defender loses the hex by default) and there is still no 'consenting' out of being invaded, both of which would ruin the competitive nature of the game and be insulting to the Attackers who instigated the invasion.
To those who say that such a policy would ruin the Attackers' initiative, I say "yes, it might". But that really shouldn't make a difference in the context of RP, I think. The Attackers still control the narrative of the invasion, the Attackers still instigate the invasion. the only thing they don't have is saying "this is starting right now!", and the only benefit I see in that is where Defenders will have to contend with multiple simultaneous invasions, wearing them out and mentally fatiguing them until they're tired of RP.
Now, to bring it back to the idea of "What experience do you want the game to provide?", I'll propose this as the experience I would assume people want in an invasion: To tell a massive and encompassing story with multiple writers. Now, the actual experience in these situations, as I see it, is anything but.
Defenders experience writing so much to keep their lot that they're worn down
Attackers experience writing with worn out writers
Neither of these experiences should be what people want. Attackers should want to write with Defenders who have the time and energy to write stories with enthusiasm, or else it's just cheapening the experience for both sides.
So I suppose the question of whether this solution is good is whether you'd rather be sieging an empty castle or you'd rather encounter and battle with present players.