Sara,
Your hub is older than mine (SL+) but I believe the construction is similar. There is a small amount of end float adjustment but nowhere near that much. How does the axle feel when you spin it in your hand? Gritty? Hanging up? Then the bearings are junk. I replaced mine myself but I have the tools. Another possibility is that the retaining clip inside has loosened or broken, leaving the bearing to slide back and forth. Hard to say by just the video. I wouldn't race it like that, although I don't think it would be dangerous unless the bearing collapsed and locked the wheel up.
I don't believe that Saris services the large hub series anymore, especially the wired SL. They should offer you a G3/G4 guts upgrade for $350. They use the existing hub but replace all of the guts including the electronics, bearings, axle, and freehub. It converts your wired hub to ANT+ wireless. This assumes that you have an ANT+ head unit like a Garmin. Give them a call and see what they'll do. Another option is that some race oriented shops will replace the bearings for you.
Good luck.