I will use my T&T 1611 (16', 11 wt) any time I am fishing big flies or heavy sink tips and I will almost always be using a RIO GrandSpey 9/10 on it for its terrific turnover characteristics.
Even though I prefer the T&T, I have cast some very nice rods recently that I also liked and which would do well in those conditions or with large flies and heavy tips. At the Sandy clave, I got to cast Robert Meiser's new 15/ 10/11 and found it is a very capable big line, big fly, heavy tip rod that cast very well. It is a rod I could be very happy with, Mr. Meisier, you got a winner big line rod in this one.
The CND Thompson Specialist at 16'7" for 10/11 lines is another one that it a very capable big fly, heavy tip, long cast rod. It is a little slower, still powerful, less stiff, and more progressive loading than the T&T and the Meiser rods mentioned above; however, it is a very good and capable rod.
The Loop Green Series 15', 11 wt is another one of those fast recovery, stiff, powerful rods with the type of action I like that I would not hesitate to recommend for big flies, heavy tips, and adverse conditions.
Finally, I got to cast a 15', 11 wt rod built on a custom Burkheimer blank for Speyrd at the Sandi clave that was another one of those nice, fast recovering, stiff, and powerful big line rods that I like. Like to above three rods, it is a delight to cast and makes casting big flies and heavy tips or casting in adverse conditions less work.
As you can see from the above, I prefer and like the fast recovering, stiff, and powerful 2-hand rods, especially in the big line models. If you like a moderately stiff rods, the above 5 may not be to your liking.