Hi folks, I have inherited a plum tree that clearly has not been looked after for many years. It is a mess of thick scaffolds going way too high (10-12ft off the ground), with groups of thin laterals sprouting from the same buds. The tree produces strongly but fruit never attains a good size and just drops.

What's a good strategy for reshaping this tree? Given that the scaffolds are 6-7" in diameter, I am afraid that if I cut them too low new ones won't grow from the tips and the tree will become a stump and die.

Any advice welcome. Photo below. Thank you!