Based on a 3 minute review, It looks like a technical disconnect between Table 4.5 and 5.10. 5.10 lists a bunch of backing material/methods, and 3.13.2 lets you use them if qualified to Clause 4. Clause 4 then goes on to apparently state that the only essential aspect of backing is omission (Table 4.5).
Should you do it, probably not.
I don't know if you will be able to stay within the parameters that are more restricted in Table 4.5 and get the weld you want. Amps, volts, and WFS are pretty tight, and I dont know that your existing procedure will have enough range to let you go from steel backing to flux without burnthrough, etc etc.