I'm only speaking as a fellow moderator, but most people don't pay attention to the moderator lists (let alone check the mod queue or posting histories), so I wouldn't worry about discouraging users.

Every team does things differently. I'd recommend reaching out to your fellow mods to mention the need for support and how you plan to identify and engage candidates for the team. It could also be something as simple as "I think we need some help, are folks fine with me inviting a few others?". If you don't hear back from anyone after a few days or a week (depending on the urgency), you can probably just go ahead with inviting folks.

Depending on how active the community is, it's also always a good idea to have some kind of a chatroom setup for this kind of coordination. Matrix works nicely since it's already integrated into Lemmy as the secure messaging option - but you can also setup a team Telegram chat or Discord server (if you go for Discord, I recommend starting your own server and keeping it closed off to your team).