I agree about the insulation. It's more important for a GH in cold country than plant beds next to the foundation. I had the same dilemma with the dense, rigid foam insulation that extends out 2 ft. from my GH base. It does reduce heat loss and that was very important, but it's also impermeable, so as much as it would have been nice to plant that space, it really wasn't practical. As it's an intrigral part of the garden, I wanted my GH site to look nice and satisfied that desire by laying timbers 2 ft. out from and around the GH at the outer edge of the foam, then filled in the space with large decorative river stone, except for a deck in front of the door, built over the same insulation, which gives the GH a nice, finished look and stones are heavy enough for me to use a vac to keep it tidy and not pick any of them up. I use the rock filled space around the remainder of the perimiter to hold large, decorative pots of easy to grow perennials, some agumented with colorful annuals and some, for veggies. (A 20 gal. pot will grow a brodacious tomato) So I get good planting depth with excellent drainage, easy maintenance, and an attractive "finish" to my GH. BTW: After the timbers were laid and effectively locked in the foam panels laying on the surface, before we added the stones, we we went all around the GH base and used Great Stuff to fill in every tiny gap, so the foam, that is under the foundation as well as down 2 ft. and then flanges out the same, is for all purposes; seamless. Every little bit helps.

Are you sure you want drainage? That will tend to keep your deck wet a lot more making it a lot more rot susceptible. If I were you I'd put foam boards down, then cement sheet on top and drain all the water into a drainhole (and possibly reuse that water somehow). If you have cement sheet you could put tiles on it for easier cleaning. Also, when you want to remove it again you can fairly easily pull it up.

can you post a pic of the area as it is now? some places look fine with a wood deck, others do not. i know MANY people who have what you describe, but it really depends on the style of the home.

You could try putting in a deep root barrier of a couple feet deep the width of the deck, though I am not certain it would work. Trumpet vines are quite vigorous in sending out suckers. You could replace it with another native, trumpet honeysuckle, Lonicera sempervirens, which doesn't sucker.