It takes me a while but eventually things will sink in. It sounds like you're welding a plate girder with the web vertical and 2 sub arc heads, one on each side of the flange/web joint, to make a CJP weld.
If that is the case, I can see why the engineer would recommend the max/min heat input test. He wants to be sure that there actually will be complete penetration at the lowest heat input.
Now, I have seen such welds being made but I have never actually welded them. So my question is, since you are using SAW, which is usually very smooth and consistent, do your parameters vary enough to be a concern? Could you run a PQR under 5.13 to qualify the roots and then use an existing PQR for the remainder of the weld (for a WPS qualified with 2 PQRs)? That would be like welding with backing for the fill and cap passes and you would have more flexibility for other WPSs.
I assume a no to this question but I'll ask anyway. Will the engineer accept a full thickness mock-up joint welded with your lowest heat input for the root, from an established PQR/WPS and do UT and macroetches?
It would seem that you will want to use your test results for future work, so in that case I believe I would push for the 5.13 PQR after all. If the engineer is concerned about poor penetration, you could draw up a chart showing what is actually allowed by the 5.13 test. As I mentioned before, the parameter window allowed is pretty small.
Hope it works out for you, I'd appreciate you keeping us posted.
Chet Guilford