Fire has a long history as a central land management tool for Aboriginal people in Tasmania; carefully controlled burns have shaped forests and savannas for both hunting and agriculture.
A. Fire has a long history as a central land management tool for Aboriginal people in Tasmania; carefully controlled burns have shaped forests and savannas for both hunting and agriculture.
B. Fire has a long history as a central land management tool for Aboriginal people in Tasmania, and carefully controlled burns, which have shaped forests and savannas for both hunting and agriculture.
C. Fire has a long history as a central land management tool for Aboriginal people in Tasmania: carefully controlled burns have shaped forests and savannas for both hunting as well as agriculture.
D. Fire, which has a long history as a central land management tool for Aboriginal people in Tasmania, has shaped forests and savannas for both hunting as well as agriculture through carefully controlled burns.
E. Fire, through carefully controlled burns, has shaped forests and savannas for both hunting and agriculture and has a long history as a central land management tool for Aboriginal people in Tasmania.
The passage wants to say that controlled fires have helped the Tasmanian people a lot in shaping their lands.
B can be faulted for being a fragment in the second part.
In C and D, 'both hunting as well as agriculture' is unidiomatic.
It's a subtle meaning issue between A and E. As one can see, the fire by itself is not the land management tool. The controlled fire is the actual tool. Per Se, E, with the rendering of the modifier 'through carefully controlled burns' as inessential, is not carrying the original intent. I would feel A is more relevant and fidel.