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I'm guessing you will find that the bottom edges of a hex tarp like the Tadpole are not long enough to provide usable doors and "a pretty wide angle of hang" will only make it worse.

You'll need...

I strongly suggest you set the hammock and tarp up and play with different tie out placements to find out what works for you. Use binder clips or a pebble under the tarp as temporary tie outs....or...