Premise:
Right now I feel a lot of people are frustrated with how localized resources work and have been since they were introduced. Although perhaps they were intended to encourage pvp, they currently encourage timer checking and logged out alts. Making the resource take enough time to collect that a meaningful competition window emerges would frankly suck to collect at all. At this point I think we should abandon making direct pvp competition a target for these. Direct competition is always a very high risk situation, and the rewards are individually not really worth risking a proper pvp character for anyone but the biggest factions anyway. Maybe it's time we look at indirect competition instead.
Suggestion:
Leaving timer/resource distribution as is, let us actually claim the resources but not via the current claiming mechanics. Instead, hearthlings would pick resource spots to dominate (need a term different from claiming since the mechanics are different imo) and would start generating authority via LP generation. I don't see anything wrong with letting someone claim multiple spots if it divided the authority among them. The hearthling with the most authority will be the only one able to collect the resource, and when the resource is collected. all authority totals are reset.
Expected impacts:
The need for throwaway alts checking timers drops. The need to immediately time and collect the resources drops as well. Large villages will gain the ability to control many of the resources in their area, but smart ones already are with alt shenanigans. In general, trying to alt this becomes difficult because you now need constant LP generation and the skills to collect something, instead of a single investment.
Hermits with small LP/hour won't be able to compete, but developed ones should be able to. There are some hermits who minmax the alt timing game who won't be happy with these changes, but I don't think that's avoidable when moving away from this system which I think most people agree is unsatisfying as a mechanic. No one else likes the "sneaker" strategy that is the main reason these players can actually get the resources.
The difficulty in alting this should help smaller villages/some hermits compete at least moderately. You effectively get "1 free resource" from any active player with the appropriate skillset, but each extra resource costs an entire duplication of curiosities. This becomes expensive quickly if you're just making characters to farm resources, while it gives value to any character you were already raising.
Issue:
This does not solve the problem of walling/claiming off the resources. I think Aceb's suggestion of unclaimed walls of any type being hand bashable with zero soak solves that personally, but it's a separate topic imo.