It actually sounds quite dangerous.
Judging from the angle I personally would have to stand viz-a-viz my BioStack bin to get anything like a weed eater into it, the risk
of a kickback from the weed eater is quite high
Something that long and that powerful has quite a bit of momentum going for it. Judge for yourself, by how much control you have to exert over that weed eater when using it on grass and such.
If you proceed with this plan, be sure to wear sturdy eye protection, ear protection, tie your hair back out of your face, tuck your shirt into your pants, wear sturdy shoes, and wear leather work gloves. Long sleeves wouldn't go amiss, either.
And be SURE someone else is nearby within shouting distance, to either help you directly or call 911 if something goes wrong.
Be sure the weed eater has a "dead-man" switch as well: if you lose control and cannot hold down the power button, a "dead-man" switch will automatically turn the machine off.
Please do NOT do this.
Compost is not a race to the finish.
When you turn your compost, fish out the large pieces then, and chop them up with pruning shears, branch loppers, or other non-powered tools.
Sunset Zone 17, USDA Zone 9