I think CBBC on Choice was often recorded waaaaay in advance, it was usually Adrian Dickson with a single camera and I can't recall a single other person presenting for about 2 years, which means they must have recorded over whatever holidays he took.
One other point about the week they spent redecorating TC9 - the breakfast show links continued to be from the old TC9, so must have been recorded in bulk for that period.
The "preview" afternoon from the new studio was TC2 as it was already built. That week they came from Blue Peter on Monday, Newsround on Tuesday, XChange (I think) on Wednesday, CBBC channel on Thursday (both TC2) and The Saturday Show on Friday. TC2 was laid out with XChange on one side and CBBC channel on the other, with a slim projection wall between the two that would often be removed if needed for camera angles. Newsround's tiny bulletin studio was round the back of the CBBC set (they once did a walk-through).
I was getting into how TV worked during this period and I used to wonder when on earth XChange got to rehearse...guessing it may have been during the Class TV strand? Unless it was in another space entirely. They did have a complicated setup to give them space though - after 1735 the channel would move into TC9 which gave them a free run in TC2 for their late programme. Later on, the channel would spend all weekend in TC9 to give Dick and Dom a free run for Da Bungalow which was obviously a major set redresss.
And yes the lifts were a nice common touch - and as many people have pointed out, the original channel set with the lift, plasma screen and doors at either end provided the basic frame for the Bungalow set build within it in TC2. Another more obvious common point was the bugs in both sets of idents but tt was only years later however I realised there was a common musical theme in the idents though. It's very subtle though. Listen at 03:05 and 03:06, that section of the melody (which appears in various forms throughout this video) is essentially the same as the bit of the CBeebies theme that often had/has "CBeebies, CBeebies" sung to it.
(00:06 and 00:07 here)