Reengaging lurkers by PM drip campaign

We’re hoping to convert lurkers to active participants, by way of PMing them on a schedule, until they convert damm*t! Actually, just a handful of PMs over the course of a month or two.

We’ve been able to ID them, and get them into a Discourse group, but the group is fairly large, roughly 13K users.

Is there a best practice for PMing large user groups, both from a performance and time-to-completion perspective? Would Discourse throttle a PM sent to 13k users? How long could that take? Should I break the send down into batches of 2k users maybe? Smaller? Larger? Across multiple days?

Thanks for your input!