around 95-97, Mark was totally found of his Les Paul and he used it on almost all songs he could, even the ones that had typical clean sound before, like The bug for example, and of course Going Home.
So I guess that in 97 when he chose to play Wild theme at Montserrat he deliberatly used the Les Paul, like he did for Going home in 96, as the intro of both tunes is the same.
During the STP promo tour, he also played Wild theme on the Les paul (bonus track on the STP maxi), and he had the 61 strat for WII, so it was obvisouly his choice , not the need to bring only one guitar
don't forget that going home on the studio version has two distinctive guitar sounds : the clean acoustic arpeggios for the intro, and the driven sound (on the shecter it seems, as seen in the clip) for the solo
during 83-86 years, he chose to play it on the strat with a clean tone to "privilege" the intro part sound, but thus the solo sound was not similar to the studio version
in 96, he cose to "privilege" the solo sound, and then it was the intro sound that wasn't the same as in studio
he could have used a stompbox to change sound, but Mark rarely used one (except in 2005 for boom like that, and 2015 too I think)
Herlock, just to be more accurate, the les Paul on the BIA tour is not the same as in solo years
In 85-86 it was a reissue model, while since 96 they are real vintage ones from 58 and 59
so the les Paul on BIA in Wembley is not the one on Wild Theme at Montserrat