Interesting question!  I think you are being very generous to be willing to take on the responsibility and expense of maintenance of the road because you use it more than others.  I hope they appreciate it.  But in my experience, some people are oblivious, and seem to just think a road maintains itself.  Other people actually do not want their road improved, for various reasons.  They may worry that vandals will have better access to their property when they are not there, or that traffic on the road will increase, or that traffic will speed by their camp, or that a better road will invite further development or raise their tax evaluation.

My suggestion would be to try to talk to each of the other landowners to see what they think.  Don't assume you know what they are thinking - ASK, and really listen to their concerns before you say anything about your own.  Then consider how you can alleviate their concerns.  Would it help to have a neighborhood watch to keep an eye on camps in the off season?  Would it help to install speed bumps?  Are they worried that you might be planning to pave the road?  Are they worried about how much they will have to pay if the road association is re-activated?  Are they worried about the liability of having work done by a resident and not by an insured contractor?  If they know you are willing to listen to what they have to say, they are likely to then be more open to your suggestions.

If the association has been inactive, I think it would be hard to accuse you of violating its terms.  But since (I assume) you do not own the whole road, they probably could say you are not allowed to maintain it where it crosses or abuts their property, so you do need to approach them with some tact.  Your willingness to accept the bigger share of the cost, and to work with their concerns, should work to your advantage.