For chest mount, try adding padding behind the plastic chest piece. As that is the part that vibrates against plastic compression suits.
if you use youtube for stabilization, it crops into your footage much like any video editor stabilization software, so try to film at the highest resolution with as many FPS as possible.
sh1tty footage can also be to low fps. always film at 50fps as a minimum.
Dont use protune unless you grade the footage. Protune simply records in a flatter picture image , which is better for grading.