11 Foot hammock, add another foot for the binners, 12 foot would be pushing it unless you set it up very tight. The Easy has a fixed ridgeline with the mossy net off that so there is a good space between the top of the mossy net and the bottom of the hammock ( even with it being a flat lay) .
I had a bit of treehugger looped on the DD along with a binner, say 15cm extra each end 2.7M hammock is a nice 3M in total which makes it 9ft 9 inch. I could get in and out of the DD with ease and while my bum was low it never touched the ground. Some one would have to do the maths for a true answer but if we think of a 3,4,5 right angled triangle 5 inch extra hammock would need a 3 inch extra high anchor. Conversely 6 inch more each end would mean the hammock dips by no more then 4 inch and I definitely had that much clearance!!
edit
re-read this and even I find it a bit garbled. Yes I think it would work for a 11ft hammock but you would have to set it tight. The gap between the two poles is not fixed, being the length of the hammock in use. The poles set up to a fixed height it is this along with the angle of droop which sets the limits.