Neither D1.1 or D1.6 cover the base metal combination you are welding.
By rights, if the contractor has an option to follow D1.1 or D1.6, the WPS should be qualified. I would opt to qualify the WPS to D1.6. Once the WPS is qualified, each welder would be qualified to that WPS using the base metal and filler metal combination used for construction.
If the contractor was permitted to use ASME, the same would still hold true unless the welders were tested using F4X filler metal. Again, the WPS would have to be qualified first.
Even if the Owner/Engineer isn't requiring the WPS to be qualified by testing, I believe it is advantageous to qualify the welders using the same welding process, base metal combination, and with the same filler metal that will be used in production.
Best regards - Al