The easiest thing to do is to hire a company that will act as the registered agent for the club. They will provide a physical address and an agent to accept service of legal and tax documents. They usually charge a few hundred dollars annually. There are some national companies that do this (like CT Corporation) but there are probably local law firms or notaries that provide this service. It's not a rewarding use of club expenses but it's just part of administration of an organization.
You don't want to use a club officer because all their info becomes public records. Also, as you change officers you'll have to refile or amend your documents every time. Failing to maintain current records with the state could jeopardize your incorporated status.
This is an appropriate response for entities that can afford it. Unfortunately, that is rarely a cost that many homebrew clubs can afford.
OP said the club was growing fast. As any organization grows the cost of administration unavoidably increases. Large businesses offering registered agent services are probably unnecessarily expensive for a homebrewing club but with some phone calls I suspect they can find somebody locally who would do it for less.
The problem with using a club member who isn't in a permanent position with the club is what to do if that person fades away from the club. The club officers have to make sure the registered agent is still involved and file an amended registration (which often costs money) every time the registered agent changes. The designed registered agent drops off the club roll and moves and the club may never know it has been served with process or received letters from the state about their filing. The club fails to maintain the state requirements for its LLC and limited liability is easily pierced. If the club doesn't act to preserve its LLC status then it's not much worth the money in the first place.
This is my main point. We don't want to tie this to any one person so the club can live on, easily, as the board changes, etc. We are researching a private agent.
As for the 501c7 registration - I understand this may not be needed now, but as we grow and take in larger sums, might not be best to just do it now? I would be curious as to what people consider the threshold for this and when it is needed.