With the kind of ranges you are talking, you may be out of luck with the handheld. 10 miles (unless the repeater is in an excellent location) is a little much for what I would expect for a rubber duckie. Sure, you could get a bigger and better "duck", but the difference will be minuscule.
And on 6 meters, consider the inefficiency of a small loaded antenna. The duck is many many times smaller than a full sized antenna and it will certainly show it in performance.
I am in a similar situation to you whereas I am in a rural area. If I am in town and can see the mountain, I can easily get into the repeater with the HT. But if I stray out of the area, I completely lose handheld coverage. But with my mobile, I can access the repeater for 100 miles in most directions.
I save my HT for listening locally and for talking with my family while 4 wheeling and hiking. If I am in a remote area, I set my radio up in my truck to act as a cross band repeater. Then I can venture several miles away from t truck and use it as a "repeater" so I can access the real repeater. Not ideal, but it works.
WM