I would ditch the hammock and use the shelter assuming the shelter also had a flat floor in addition to the three sides and roof.
If I can get a firm and flat surface to lay on I will always choose it over a hammock. I would only use a hammock to avoid rocks and roots and uneven ground and also to save weight over a tent. Saving the weight of the hammock by using the shelter is an added bonus.
Regards,
CB
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