The lawn mowings will work fine as long as you add enough browns to the mix, if you don't they will compact and go anaerobic which is not a good thing, to many bad bacteria will thrive in the no air environment.
The more stable bedding and manure you can get, the better. Even better would be to mix the bedding and manure with your mowings and
compost that for around 3 months before using it for hugel topper material.
using manures in compost heaps builds a great biosphere where bacteria and fungi love to live, this means you will have all the goodies growing where you want them when you cover your hugels with it.
Definitely do not disturb the bog or do as little disturbing as possible, that is a wonderful thing all on its own.
Once you have a hugel covered with your life rich compost, plant the things you want to eat or grow. They will thrive.
Redhawk