I hope you get your stats sorted. However, of course, this doesn't remove the inconvenience to your members, only reduces it.
Since you have a large and active forum, I suggest putting up a banner notice at the top of the forum which shows on every page (you can do it in the ACP, it's a standard function) advising that on xx date and time the forum will be closed for maintenance and apologise for the inconvenience. Don't elaborate on what that maintenance is, for security reasons. I suggest making this notice period a week. As it gets nearer the time, say, 24 hours, update the message to say that the maintenance window is approaching and to log out before then or data will be lost.
At the time of the upgrade, close the forum to visitors and then run the upgrade. Note that just running the upgrade will autoclose it for the duration, but you should remain in control of this, especially if it doesn't work properly afterwards. Thankfully, XF updates tend to be quite quick.
Finally, make sure that you take a backup of your server and database just before and just after the upgrade to help with disaster recovery should it happen.
Good luck.