Saturday Starts Here was a strange thing. CBBC continuity but done by the Going Live team, often from outside the studio as I recall.
I'm not convinced it was live. The Going Live studio would have better things to do than continuity links in the run up to a three hour live show. Much easier to stick the links on tape during the week and let NC1 play them out.
As you mention, initially it was indeed part of Going Live, with the links from around the studio, and Going Live was billed as a part of it -
https://genome.ch.bbc.co.uk/schedules/bbcone/london/1987-09-26
But as you suggest, it probably wasn't live. Although Pip and Saz are billed there, for most of the time it was Peter Simon and/or Trevor and Simon doing it, and in those days Peter Simon was usually in the studio during Going Live, presumably for continuity purposes, that also being the era Double Dare was much more integrated into the programme with the set looking very similar to the Going Live set, as opposed to later years when it was clearly a pre-record and looked totally different, with Peter Simon rarely seen on the rest of the show.
One I vividly remember was one morning when Trevor and Simon were supposed to be getting the studio ready, but accidentally demolished it and had to rebuild it, and then on Going Live they were in an odd-looking studio for the start of the show, I remember them sat on directors' chairs in front of a desk. For ages I assumed there was a strike on and they had to use a studio dressed for another show, and that was how they covered it, but seemingly not as I've seen quite a bit of that Going Live and after the first cartoon it's all back to normal. Seemed a very elaborate joke, I don't know what the context was.
Then after two years of that, as you mention, Saturday Starts Here was revamped, started earlier (at 7.30 rather than 8.30) and was totally self-contained, with Wayne Jackman and Clive the kangaroo doing the links -
https://genome.ch.bbc.co.uk/schedules/bbcone/london/1989-10-07
One interesting thing about that year was that during the Commonwealth Games it moved over to BBC2, with Going Live staying on BBC1, which wasn't usually the case -
https://genome.ch.bbc.co.uk/schedules/bbctwo/england/1990-01-27 I remember Jackman doing a bit of business with a lever with BBC1 and BBC2 on it. Funny the things, eh?
All this was only in the winter, of course, and in the summer it would be the usual on-duty announcer, which became the case again all year round between 1990 and 1992.
One of the other things I remember about that period was that the OU programme immediately before the kids shows was a course on geometry, and because I was an awful kid who woke up stupidly early, I used to see most of it (I was such a Beeb kid at that point it didn't matter if there were kids' shows on TV-am or C4, I would rather have watched the Open University), and I think a week or two after the new globe launched, they did quite a long sequence about the COW and how that worked.