Which metering mode do you use?I would handle this in exactly the opposite way to you!
First if I used a "Priority" mode it would be Shutter Priority and I would set my S/S to the same number as my focal length (so 1/500 sec. at a minimum with that lens) — and four times that if fast action is involved.
My normal method is to shoot in Manual Mode with Auto ISO and mostly to use my lens fairly wide open.
Next, because I only ever shoot RAW, and because the internal metering on every Nikon that I have ever met systematically under-exposes by 2/3 of a stop, I set my Exposure Meters (via the menus) to plus 0.7 EV. That gets my shadows well away from the left-wall of the histogram and decreases Noise considerably.
Don't worry about the HLs, because you have more headroom than you probably realise; and, on a dreary day with flat lighting, you have very limited DR anyway.
Try doing that and see if it helps.