Remove all the mulch. Whatever price you use to install the mulch charge that price for the removal plus a hauling fee per load.
Next survey the root system of the plants involved.
You will not get stone to lay down and smooth out like mulch.
Areas that have large roots exposed you will need to build the grade gradually to cover them.This could cause you to use more stone than you calculated.
The stone bed should drop a few inches in grade through out the beds.
Remove excess soil to achieve this as needed. You will need to have a good edge to hold the stone in the bed.
Next apply the fabric of choice,be careful not to strangle the plants with it.
Too much next to plants can repel the water and cause the plants to dry out. I use the U Staples ( the kind you find in the electrical aisle) to hold the fabric tight to the ground,I just pound them in with a hammer.
The apply the stone evenly throughout.
This job can be labor intensive, I personally do not like it but if that's what pays the bills.