If it is for a structural application, the Owner, through the Engineer can expand the scope of D1.1 to include thinner materials, unlisted materials, etc. That being the case, Engineer can make the necessary modification to D1.1 and use it where it is applicable. Where D1.1 doesn't meet the needs of the Owner, modify D1.1 so that it will work.

For example; you are using an AISI material that is not listed. Include the unlisted material as prequalified if it is low carbon (0.3%) steel. If the undercut provisions are too lenient, tighten up on the limitations. If the root opening or the joint details do not work for your application, they too can be included per D1.1 provided the Engineer (representing the Owner) concurs. If you need to restrict the amount a weld can be oversized, add it to the engineering requirements and acceptance criteria. If you need the intermittent welds to be located within 1/2 inch of the "ideal", add the new requirement to the engineering requirements, acceptance criteria, etc.

Normally, structural projects would simply include the new or modified requirements in the project specifications. This doesn't sound like a typical steel structure, i.e., a building. Maybe this is for some small item that is being built in-house. It doesn't matter as long as the new engineering requirements and acceptance criteria are noted where they will be seen by whoever is actually constructing it.

By the way, even the qualification requirements can be modified by the Engineer. You cannot do reduced section tensile tests as described in D1.1? Have the Engineer change the reduced section tensile tests to full section tensile tests. Instead of welding one sample, weld the number of samples needed to suit the Engineer's requirements. 

It goes without saying that the Engineer needs to carefully consider the implications of any code modifications before instituting the changes.

Al