In my opinion, Tables 3.1 and 3.2 apply strictly to welding, as do the notes with regard to heat limitations of 5.7 not applying to A913 steel. I believe this is because the A913 steel is not as susceptable to the heat degradation generated by welding as the other quenched and tempered steels are.
Oxygen gouging and carbon arc gouging are basically two different processes. I think there's more heat input associated with oxygen gouging than with carbon arc gouging, which may be the reason that oxygen gouging is not permitted. If that's true, the heat of the steel that's generated from oxygen gouging will cool slower than that of carbon arc gouging, and slower cooling of quenched and tempered steels is not recommended.
If you're not satisfied with either of those answers, if you can find out the mill's recommendation for maximum heat input on A913, compare it to that of the carbon arc gouging process. If heat from gouging is lower than the recommendation, you may have something that you can run by the EOR.
I have no facts to base any of this on. It's all just my opinion.