Got it. So, if the exotic invasive honeysuckles are present, then yes, they will happily move in to fill any newly-created space. Again, I'm right there with you, having dealt with numerous similar situations. You're on the right track in knowing that nature abhors a vacuum. as soon as one element is removed, something is going to move in and fill that spot. So, are you at all familiar with the cut-stump, or as I prefer to call it, cut/treat method of removing and eradicating non-native invasive woody species? We've talked at length about it here and elsewhere, so some kind of search should turn something up. That's the technique you're going to need to use if you are to have any hope of beating this honeysuckle back. It is doable. I get what you're asking, that of the possibility of the conifers appearing too stiff. I happen to like conifers a great deal, under the right conditions, and my favorite woods have both broadleaf and coniferous species. One thing that can help to soften the effect is to plant in groves, the way nature usually does. So, in nature, some disturbance-fire, windstorm, etc. -would have cleared an area. Often, conifers are among those species able to colonize such sites. As such, they are often quite closely-space initially, with the stragglers dying out over time. What is left is a rather dense grove, especially true of the genus Thuja, which is what the Green giants are. I'd rather see a grouping of them than one blob here, one blob there. I'm sure you don't have any native groves of Thuja occidentalis down your way, but up here, it is a common feature of primarily low, wet woods. And everybody-and I do mean everybody-loves the effect of these groves. From any distance at all, it looks like big, oversized moss to me. In any case, that is the type of effect I'd go for with the GG's. +oM

The groundcover you choose will depend on where you are and your requirements. If you have a mulched path through the side yard, then your options open a little to include a groundcover not especially tolerant of being walked on. If you have no mulched path, you'd need a more durable groundcover. It should be low whatever it is. The Hostas at the house are fine. Make the bed for them deeper and plant/increase them such that they are less spotty. Instead of with a fence, you could screen with a tallish hedge or an extended trellis of vine. Either will require light in order to grow well, and space (especially the hedge.) The trees then present a problem because they've been allowed to grow with those low limbs, which will be in the way and will add shade. No doubt, the tree would have had vastly better form had these been removed when young. We can't see the tree's head so no opinion on the form if these were removed now. But since it's the side yard, it's probably not too critical. Too, your neighbor's tree has low branches/limbs hanging over the property line and these will add more shade. You have the right to remove these back to the property line, whether your neighbor agrees with it or not, as he cannot control your property by placing things in it. Most people would be polite and inform him of their desire to remove the limbs and give him the opportunity to do it himself, if he wished. You'll need the light in order to succeed with your project. If you don't have it, new plantings will likely just eke by, looking weak and thin.

If you go the trellis route, build a frame for it, like a big picture frame, so it won't look cheap. Then hang it from the upper beam, and connect it to the lower beam by a couple of links of chain so it doesn't swing in a strong wind. If you paint or stain it the lightest color that will go with your exterior paint scheme, the reflected light when viewed from the neighbor's direction will make it hard for them to see through. It will give you even more privacy than you feel you are getting. You could try planting annual vines like morning glories or trailing nasturtiums or dipladenia to give your neighbors a colorful treat. I have bamboo blinds. They blow wildly in the wind. I don't care if they swing outward, but I don't want them swinging inward and whacking someone or sweeping everything off the table. Solution: two screw eyes in the beam above, two in the railing below, connected by a couple pieces of picture-hanging wire, so they can't swing inward. Curtains are lovely, and the light they radiate when the sun strikes them is gorgeous, but, if your climate is humid, you can end up with black mildew and the need to launder them frequently. That looks like a lovely deck, so I hope you find the solution that makes it a joy to spend time on. Enjoy a tall glass of lemonade for all of us! :-)

For privacy in 5B, I've done a mix of arborvitae and privet, strategically placing the evergreens where privacy is needed year round. Specimens or anchors with spruces. For 15'ish high used "Techny/Mission" arborvitae, but "Emerald Green" is popular and sold everywhere. "Fat Albert" blue spruce. "Cheyenne" privet (seems hardier with long cold spells). Higher than that then "Green Giant" arborvitae and "Columnar" spruces.