After all these years I'd not spotted that there was any pickup changing involved but the Crackerjack video clearly demonstrates both audibly and visually the opening bars played using the middle pickup, thence switching to the bridge for the other parts you mentioned.
This got me thinking so I just played the original record and I'm really not sure even now which pickup was used for those opening bars - sounds slightly more like the bridge to me but then if that were the case why would Hank switch pickups in the Crackerjack piece if he hadn't recorded it that way in the first place and make it harder for himself to play live? Later concert appearances suggest he used the bridge throughout but then he was using it for most tunes anyway by then. Hmmm - got me intrigued now . . .
Interesting how a casual enquiry by Ian could upset my memory's applecart but with the passage of time, the old memory isn't what it once was . . .