I haven’t fully cracked this code yet, as it’s some specifically an objective. We’ve been fortunate enough to unlock mostly non-staff replies and answers. 

But what works for me, regardless of department, is usually bringing the community to my colleagues in Slack, where they work most of the time. AND to only ask them to focus on questions that haven’t received any replies.

So rather than asking them to browse the community or monitor the firehouse of posts, it’s more intentional in ask. Plus, that can be tied to things like company values or commitments to a positive customer experience. And you have data you can leverage for your argument. “We want our customers to have a positive experience, yes? We want them to be successful, yes? Well, these X% of questions are getting lost if they go unreplied for more than Y time period.” (Not sure that’ll solve your SLA challenge for the metrics they care about most...) 

I’ve applied my approach in a multi-level way via Zapier automations. 

• Level 0 - let the community have first crack 
• Level 1 - alerts on weekdays for questions that have hit 12+ hours without a reply (our data showed these were likely to be buried and missed)
• Level 2 - alerts on weekdays for questions that have gone 72+ hours without a reply + automations to reply to the post (bumping it in the feed), toggle it sticky, and then added gamification around this
• Level 3 - manual asks to internal subject matter experts, but usually if the question is clearly something that others couldn’t answer

As part of this, I also leverage “watch a tag” channels for specific teams to only monitor questions related to their areas of expertise. This narrows down the asks even further. 

Here’s the end result of our experience. 

If you focus not on the green space of the charts above, but the grey, you can see that the percentage of asks to staff is pretty modest (30% for the initial ask, 12% for the second ask). 

I don’t know if that’d work for you, but my hope is that narrowing down your ask to your colleague might help weaken their primary argument: “too much time away from the queue and impact on their metrics.” 

Another thing that might help: try to find a way to show the likelihood an unanswered question becomes a support ticket anyway. 

In that way, you’re actually saying that their help will reduce the queue and mitigate the impact they’re worried about. And it’s a much better customer experience for things to get answered the first time.