One method used in pheasant flight pen construction is to install a couple tall (telephone poles) posts deep into the ground and braced well (flight pens could be 15' tall). Then, cable is run between the posts, with pulleys, to support the netting and a crank is installed on one end. The netting can then be dropped in case of an ice storm and then cranked back up.
I'm not too familiar with vines but I assume they need to crawl/grow up something? Could you bury your posts 2' and use them to support the vines to a height of 4'? You could have the cable lowered to catch the vines and then as they grow crank the cable up to the 5.5-6' height? With the amount of constant weight on them, you may want to install some intermediate posts.
I don't have the cable set up on my flight pens, which is why they have collapsed 3 times in the last year (snow/ice) and I am retiring from the aviculture industry. However, I have been trying to think of ways to use my enclosed pens and the investment I have out there. This may be something I might look into. Also, I have access to thousands of 6' posts being a guardrail contractor. Let me know what you come up with. Thanks!