Just to paraphrase, your main goals are to reduce the amount of dryness and to carbonate (in the bottle.)
If the concentrate is fully fermentable, then adding more concentrate can only help you achieve one of goals but not both at the same time:
- With the unfermented concentrate in the must add potassium sorbate to halt fermentation, leaving unfermented sugars in the must. You get sweetness, but no carbonation, since the yeast are inhibited by the sorbate, and can't ferment in the bottle.
- You can bottle, and let the yeast ferment the concentrate to provide carbonation. You get carbonation, but not the residual sweetness. (And since the quantity is presumably unknown, you risk overcarbing or exploding bottles.)
To add sweetness, you can add food grade glycerin. This adds sweetness and body, and is often used in winemaking.
In principle, you could then bottle with the concentrate already added as priming sugar. However, I wouldn't do that since you don't know how much CO2 will be released, risking potentially exploding bottles. Instead, ferment out the added concentrate - raise the temperature a few degrees and then gently rouse the yeast to help kick start fermentation, and If that doesn't work, pitch some more yeast.
Once the yeast have fermented out the concentrate, rack to a bottling bucket with added priming sugar - you can calculate how much priming sugar to use to reach 2.5-3.0 volumes of CO2. Then bottle away - the amount of priming sugar is known, so no bottle bombs!