It would be nice if there was an option to advance to the next slide when the video ends, but without that you're down to improvisation :)
The 'best' solution depends on a few different things
The 'easy' option may depend a lot on the nature of the video - if it's full motion, or a series of cuts.
If there's any points in the video that make sense to 'cut', you could slice the video into separate chunks and tie them together on separate slides. I'm not sure where you're seeing 99 seconds, but on my machine (MacOS 15.2, Keynote 14.2) I can set slides to automatically transition up to 600 seconds (10 minutes)... on that basis you'd only need to cut the video into two 8-minute segments, and have the second slide automatically start after 8 minutes.
This approach isn't likely to work for full-motion video (since the cut would likely be visible) but if there's any sequence in the video where you can slice it, this may be an option, even if you have to do multiple slices. They don't have to be equal sized, of course, so it depends on where the cuts in your video (if any) are.
The second option relies on the fact that the Keynote duration is largely a UI restriction - OMM I can specify a Transition with up to 600 seconds, but that limit is because of the UI, not any hard restriction (at least that I can see).
What that means is that it's possible to poke 'under the hood' to set a transition time that's longer than the UI lets you specify.
For this, I used AppleScript to directly set the delay on slide 2 of the current document to 960 seconds
tell application "Keynote"
tell document 1
tell its slide 2
set its transition properties to {automatic transition:true, transition delay:960}
end tell
end tell
end tell
Now this slide will automatically transition after 960 seconds. I have no idea what the upper bounds of this value is (I didn't have time to test hours, but see no reason why it wouldn't work for larger values)

The downside is that you risk losing the setting any time you edit the slide, so you may have to re-apply. Fortunately it's not hard to do.