The upgrade documentation assumes you are not migrating to a new server machine or SQL instance. However, many customers want to do hardware & software upgrades at the same time. This makes it a little more complex and adds a few gotcha's. Here's what I do (In addition to everything in the upgrade PDF):
It sounds like you want SLX to continue to be available to users (probably read only) while you perform the upgrade and testing. If that's the case, do not upgrade the production database on the old server since once you begin, the 6.2 client will no longer work. These steps also assume you moving the SLX Services to a new machine
1) Backup the production DB. Announce to users that SLX should be considered Read Only until their workstations are upgraded. Have someone run around and tell them in person because someone always shows up after the upgrade and wants to know what happened to all the stuff they entered after the "SLX is Read Only!" email was sent.
2) Restore the backup on the same SQL instance and set it up in Connection Manager using different name.
3) Run the first database upgrade step on the copy you set up. This has to be done on a machine with the 6.2 provider installed.
4) Make a backup of of the upgraded copy and restore it on the new server.
5) If you are also moving the logging and documents folders, copy these to the new server.
6) After installing the Admin workstation as described in the PDF, launch Admin and set the logging and document paths to the new location.
7) Proceed with the upgrade as described in the Upgrade PDF.
8) After upgrading the workstations, shut down the SLX Server service on the old server. If any workstations were forgotten, you want them to call right away, not work for two weeks in the old DB and then wonder why no one can see their changes.
9) If there are remote users, be prepared to cut new databases. I have successfully upgraded 6.2 to 7.5.1 remotes without cutting new remotes when using the same server, but whenever I've migrated to new servers while installing an upgrade, the remotes were all corrupted and had to be recut. If anyone has figured out how to do that please post how.