don't allow them to censor at all, let vote system take care of it.

I basically agree with /u/trevmon.

A bit of level setting with the mods from a public booing from the admin and other mods will typically do the trick. It may have been a better idea to pm the mod with a set of admin expectations of future mods.

Is this deletion issue/concern something that you identified yourself?
Or, were you notified of the deletions by someone and encouraged to consider action?

A) If this is something that you personally identified, then I'm confident in your judgment and experience. Deciding that your operation needs a new procedure/rule, is your prerogative.

B) However, if someone contacted you about a new sub posting suspiciously high volume of posts, and then deleting multiple comments; which is likely to draw attention, then that it's a different situation. I'd recommend stepping back for a second and critically assessing the progression of events for any problem-solution-reaction style activity.

C) Error on the side of caution, and go ahead and critically assess the progression of events for a problem-solution-reaction style activity anyway for scenario "A" just to be safe.. There's no downside.

I'm much more concerned about the consequences of the accumulation of many small well-intentioned rules.
Multiple small rules can accumulate and create a moderation technical disaster.

Whenever possible, it's better to have a self-policing culture. This won't happen if mods are policed. However, if certain mods do not demonstrate the necessary set of free speech principles then those cases will have to dealt with based on the situation.

It's worth considering that the Reddit mods that we criticize, are doing exactly what the admins are requiring of them. This is a fact.
Corporate Reddit is pleased with the activities of the current/remaining mods.

In this very way the moderator culture will be what you make of it, or accept from it.

Conversely, the general community will learn to get out the pitchforks if doing so continues to be an effective strategy for creating changes that various outspoken community members may eventually push for.
This isn't meant as a criticism of anyone, as it is human nature.

Just saying.

Fortunately, the community is still small enough that you can address new mods in a direct and earnest manner.

I'd recommend a free speech authoritarian approach.
It may sound like a contradiction, but that captures the reality of your position. I respect that you don't seem to like/want this degree of responsibility.
Fortunately for the rest of us, this makes both you and d3rr eminently qualified and capable. You gentlemen are two of the few who deserve it.

• Free speech is the priority.
  
• Minimal rules/constrains
• Voting takes care of the majority of issues.
• Mods ensure content is relevant; deletion minimized but used for clearly defined criteria {other than a single dank meme™ exclusion}
  
• Admins deal with mods.
  

I would like to suggest creating an admin rules log that contains specifics about the antecedent factors that led to any given future rule, or even the discussion of rule implementation even it it didn't get implemented.
It's useful when looking back at previous events to know the history.

I would recommend that you and d3rr should do this, but keep it private.
It could be examined and used by some group to conspire to pull the strategic problem-solution-reaction playbook; in the same way that you could use it to plan for what had worked in the past.

I might sound a bit paranoid about all of this, but who cares about my paranoia. Privacy exists for a reason. It should be valued.