Mixing Compost

Hi …. My local council offer free ‘compost’ ……. It’s not quite the soft brown sweet smelling stuff you buy in a garden centre ………. It’s black, can contain ash (sometimes still hot)
It contains a lot of rotted stem & stalk that can be thickness of a finger and a couple of inches long.
I have taken about 3 tonne in past 3 years mix it in with rotted cattle manure, and seaweed form local beach, and it has transformed my clay rich heavy solid into a very good growing medium – and its free, as much as you want.
As I rotate each growing area to potatoes have prepared the bed with this dual mix.

My question is has anybody come up with a decent way to mix composts, I have just  filled up 4 of  the large 3330L bins with my own garden waste and this council compost …. Hoping the heat & mass of the imported compost will accelerate breakdown of my garden waste.
What I would like to do is then find some way to chop/shred/mix it  ………  just to get  it to reasonable size before incorporating into the garden. 

When it is in the ground I have in the past run a Mantis back and for and that does work …….. just wondered if anybody has found a way before I put it in the ground.
I did wonder about just emptying bins and trying tiller on those, but expect  it would be thrown everywhere.
I do have a branch shredder … but assume this would clog if I tried putting compost in.

I do have a 25 gall plastic cold water tank use for rain water ... I could use that as a pot to mix using the mantis.

Just seem to think the compost will be all the  better if I can get it 'shredded' and mixed.

The Mantis does chop it well when used in the ground .... maybe I'll try it in water tank ...just think it might clog if not moving fwd