And while a "true" lycanthrope may only have its full powers for ~2 months worth of days per year, they're at least spread out.  It's much easier to weave a game around them.  It may be fine mechanically, but make sure the character knows what they're getting into if they're going to have extremely long periods of game-time of weaker-than-human status interspersed with periods of super-human cool-ness.  I know I for one would just not enjoy the character.

I agree, I also don't think I would enjoy the character. The problem is that Lycanthrope provides inherent tension and interest for the entire group. It is an ever-present story element that they players and GM have to work with and around.

Meanwhile with the Arkanthrope there is basically only 1 month a year, the two weeks surrounding the losing of power, and the 2 weeks surrounding the gaining of power, that are filled with tension because of this same issue. The rest of the time he either has the power, or doesn't have it, and there is no need to think or worry about what might have been, or might soon be.

This pretty much takes all the fun out of the situation. I say go with the Moon phases.

Alternatively, make the Arkanthrope powers Crepuscular, like many bears tend to be in the wild, active at dawn and dusk. So they would be active for about 3 hours in the early morning and 3 hours in the late evening. That is 6 hours of 24, making them active 25% of the time, so not too far off Lycanthropes active percentage. Then the tension is then built around what time it is, rather than what day. Could be quite interesting to actually play.

I actually don't see a problem at all. You have a lot of semi-connected facts that you are interpreting as ultimately leading to a final battle where the walls fall, all heck breaks loose in the city, and the story (campaign) effectively comes to an end. I don't see this at all. You have a MILLION things you could do with all this with a multitude of possible conclusions, none of which ends the campaign.

*A story line that resolves the threat without failed walls, and does so within the power limits of the PCs and their allies, but of course creates a new threat that is even greater.
*A story line that resolves the threat by having the walls fail and the "something" win or lose. This could be either a small portion of the walls in both a physical and magical sense, the entire thing in only a magical sense (so mundanes don't see it), or the entire thing in a physical and magical sense. No matter which it is the failed wall will massively change either a threat or theme of the city, or both, giving you plenty of new stories to play through.
*A series of sub-plots or stories that never resolve anything. This thing has presumably been outside the walls for 800 years. If it hasn't made it in yet then there is no need for it to make it in during the course of your campaign, or certainly no time remotely soon. This could be the PCs un-named and ultimate nemesis that they don't even realize they are fighting against most of the time because its plots are subtle and involve many other faces in the city. As a matter of fact EVERYTHING could be affected in some way by this unseen enemy that is never directly confronted. Over many years (game time) the PCs would slowly realize just how many times they were really fighting against this things attempts to enter the city, but they would also realize a direct confrontation would never resolve this. It is just an endless game they have to deal with as best they can, and be prepared to pass the torch to the next generation when their time is up.

Other thoughts:

    * A threat with the aspect "Something hungers beyond the Outer Gates"
    * an ancient being (who appears to be an old woman but has immense power) who it is said hasn't left York since the C12th because if she did the walls would fall (and may actually be the Roman Godess Cybele !!).
    * an ancient prophecy who believe that when Yorkshire falls to the thing from Beyond the Outer gates, that within Yorks walls alone will stand and the defenders of Yorkshire will rally there.

Perhaps you could have a series of storyline(s) where if the PCs (eventually) fail to stop someone (the ectomancer, a misguided RCV, etc.) then a portion of the wall fails and this thing enters. The PCs then have to try and stop it from finding the beacon, which is actually the ancient old lady that is one of the PCs friends, and which is helpless on her own against the hungry being (it is her achilles heal of sorts). Fortunately it is not that strong yet because of its been hungry for 800 years! So the PCs are strong enough to beat and destroy it, if they manage to track it down. It will be using pawns it controls once in the city to help it figure out who and where the "beacon" woman is, so that provides a storyline after the wall has failed. If they players do destroy it then the threat from it is ended. If they don't stop it then a very powerful being is unleashed on the city and they have to convince all the factions of the city to work together to destroy it (or weaken it and trap it somewhere), changing the power structure of the city when they succeed (important people die, and the remaining have also worked together, changing their view of each other just a little). Obviously no matter when it is beaten it changes the threat and themes of the city, keeping the story going.

    * a city enclosed within city walls which act as a threshold to supernatural creatures (and wizards),
    * a single gate which is the only way supernatural creatures can enter/leave the area enclosed by the c12th city walls,

If the thing gets in as detailed above, then there is the question of what to do about the new hole in the wall. Perhaps the reason for the wall in the first place was actually that the city is particularly close to a very wild portion of Nevernever in many locations. With the wall down there are numerous new places that creatures from Nevernever can come through, and so these random wild Nevernever creatures are the new major threat. The PCs have to deal with this threat while also trying to figure out how to rebuild the wall, possibly against the wishes (and efforts) of certain other established factions that find the increased chaos and fear created by the Nevernever creatures to be in their favor. Perhaps WCV's that feed on fear even move to the city because of the ridiculous level of fear.
   
    * and finally a cult lead by a Ectomancer who things she is hearing her dead husbands voice but is actually talking to something from beyond the Outer Gates bent upon bringing about that prophecy

This is just the kicking off point for your first story based around the "something" trying to get in. Once the players beat this lady the thing will come up with a new method to try and get in, providing many storylines to come.