I think you're right it's glued on. Good idea on chiseling some pieces off to lighten the load. I honestly don't know if even 4 or 5 guys can lift this thing. Someone suggested creating some kind of wedge to help raise it as well.
My thought:
- cut a thick piece of plywood to size (3' by 3'?) Wide enough for grip ...maybe even buy some sort of handles and screw them on the sides to allow for grip/leverage.
- set prop boards along existing base about equal to height of remaining base layers (some 2x4s screwed together?).
- in some manner, slide plywood under the downed section. Probably need to use crowbars and 2x4s to lift a side of the downed section in order to get plywood underneath by coming in from the side.
- if you can get the downed section on the plywood, then lift the base of the plywood (with downed section resting on it) onto the prop boards.
- chip off old mortar from good base, and apply new mortar.
- angle the top of the plywood so the downed section is raised up and drops back onto the good base.
But I don't think this will work.

As the very heavy downed section drops back onto the good base (assuming you can get to that point and get it to 'drop' back in place perfectly), the weight will squeeze out the new mortar. And I don't think you can set it back in place by coming in from a side angle. At some point, you'd probably need some lift to come almost straight down.