Hello Doc:
In the 4.2.4 numeral of the AWS D1.1-96 Code you are refered to the Figures 4.1 and 4.2 in order to determine wich your production position is, and for other side, it refere another figures (4.3, 4.4, 4.5 and 4.6) for test assemblies both for WPS and personnel qualification. As you said in your post, in that figures you can find, for the 2G position, the notes: Plates Vertical and Axis of weld horizontal. Then, I think that you may to pay attention to these requeriments.
However, if you need a better control of your puddle and you have a partial or complet joint penetration (PJP or CJP) cumplying with the requirements of 3.12 or 3.13, you can qualify your WPS using a CJP wich helps you in your interest, I mean, you can use, for example, a double bevel groove weld (instead a double vee g.w.) wich has an AWS designation B-U5a for SMAW (see Figure 3.4) and you are still cumplying the Code. In that kind of groove, only the top element has a bevel and the square edge of the lower element helps to mantain your puddle in horizontal position. Take a look too, to the figure 4.29 for a similar application in welder qualification.
I hope this help you.
Jorge Giraldo
MedellĂn, Colombia