Reading this part, I came up with an idea to change the feature, so I took some inspiration from the feedback already provided. Also the % are made up.
Instead of resetting all the perks to 0, they could loose some progress every week. You could completely remove the 3 week cycle. I think the idea can be best explained by an example:
Let's say initially there are 10 perks to choose from. You can contribute to any perk you want and a maximum of 3 perks can be activated. So far it is the same. Instead of separating the 3 levels into separate bars, have one bar with 3 milestones: One for level 1, one for level 2 and one for level 3. This might sound minor, but is important for this one: After the first week your guild looses 10% of progress for every perk, with always a minimum of 100k points. After that calculation, every perk with 0 progress will be exchanged with another, new one. After the second week all perks, that stayed will loose 20% of their progress and the others only 10%. So after each week every perk that stayed will loose 10% more progress. This is important, because guilds should change their perks around a bit and not have the same 3 perks every week. How much progress a perk will loose could be shown, when you click on the perk to see the details.
If you want to change it to happen every 3rd week (to stay at the initial 3 week cycle, so that you don't get too many new perks in a short amount of time), you can just increase the percentages, to like 20% (which would mean a guild would have a perk for max 5 cycles, but to keep it, it will be very expansive).
To avoid being stuck with a perk you leveled and don't want the huge drawback next cycle, you could maybe have an option to mark a perk as 'exchange', so it will be removed in the next cycle. This one could be bound to guild leaders.
To expand on the 'specialization' part: It would be a good idea to show the current active perks in the guild profile. If you click on it you get information on what level this perk currently is and what the benefits are.