It probably won't drop much lower, if at all. Meads tend to end up somewhere around 1.000 +/- 0.003, though that can vary depending on the honey, yeast, any fruits, etc. Not like wines that can reach 0.992.
I personally find that back sweetening is a much more reliable method to use than trying to arrest the fermentation. Just make sure you stabilize the mead with sulfite and sorbate before adding any sugar or honey for final sweetening.
No harsh flavors is great for your first try, especially as you fermented during the warm months. I'm guessing you had some form of temperature control.