Depending on your timeline, you could do this with virtually zero downtime. Rather than doing a bulk copy, you could easily chunk this up since you're not looking for updates but only inserts (if I understand you correctly.) Just select top (1) id from the new table and then get the next N records from the old table after that ID to do the insert. Wrap each iteration in its own transaction, add a maxdop of whatever makes you comfortable (for something like this I would typically use 25% of my processors on a busy machine) and include a short WAITFOR DELAY after each iteration. With such a strategy you can easily plow through the copy without adversely affecting your server. You will still need to have a very short period of downtime to rename the old and then make sure you didn't miss any new records coming in before you rename the new, but it will be a matter of seconds instead of an hour.

If you're not worried about the downtime so much, I believe the plan you have established will work fine.