It depends on how your tree is structured but I usually don’t recommend stumping a tree to change over the variety. If your tree has good scaffold branches, I would try to keep them.
Simon
All the cocktail and variety changes I've done where I've tried to maintain the tree size or shape have been problematic. You need to plan for their future growth to fruiting size, so around 6-8' of growth from where you graft them. I can agree that saving the scaffolds is a good idea, but leaving say, 8-12" of length to each branch, no more.
One of my first cocktail projects, a rootstock pomelo that had been grown to a full size citrus tree, the owner asked me to keep the tree the same size, but add varieties. Now, it is awful and lanky and you can't prune anything because the grafts start so far outboard.
MasOlas, if this were my tree, I would not hesitate to take the branches down to 12" from the trunk, then choose your sprouts to graft onto next year. Being that it's cold now in SoCal, and soon to be rainy, I would probably wait till Spring to do this pruning when you can reliably get some vegetative growth. This said, I'd love to hear from some of the FL growers who have more experience with this type of activity.
Skhan had some videos or threads about topping his mangoes years ago, and I was simply amazed when I visited this year to see how massive and productive those grafts had become.