Adding more glue doesn't do anything for performance(except take from it) and will scare the heck out of you when it starts popping as you draw the bow. After the first layer of sinew I go back with slightly shorter sinew to fill the void and when that dries(visually, not completely) I add even shorter sinew to fill any voids. Once the glue gels I'll take a smooth object and smooth out any humps.
You can use hide glue to add the cover too. Sinew/hide glue is heavier than the wood so you want only enough to do the job.
To get the glue to adhere to the older sinew lightly sand it, size it with warm hide glue, let it set and size it again then add more sinew or your covering. If you think you have finger prints on the back you can wash the sinew backing with detergent and rinse with warm water just before adding more sinew or the covering.