The "Dolly had braces" Moonraker psyop was a massive government trial operation to gaslight the world and test out their information hygiene.
The Kennedy assassination response ended up as fucking chaos, but sufficient chaos to muddy the waters. Enough of the public basically realizes though we live in a fraudulent government which is why half don't even vote.

So they wanted a tighter "Mandela Effect" which is not a particle accelerator, but a massive army of agents and listening channels.
Literally listening for media posts of people with old copies of VHS and so forth to find who has them, intercept and replace them, all without anyone knowing.

They used this machine for the Reagan assassination. He was assassinated, but they Mandela'd it so hard we don't even REMEMBER what the alternate reality was.

Mandela's death in prison was not the same protocol, but an inferior MI6 version copied off of it. Hence the name of the effect is appropriate.

This might make the government seem monolithic and almost all powerful. But the resources to pull off one clean Mandela effect rival the space program in budget.