I believe the "law of God" (Rom 7:22) to which Paul refereed was the will of God or the fulfilling of the OT law which, "was our schoolmaster" (for the Jew) to bring them "unto Christ"; also which they "are no longer under" (Gal 3:24, 25). The "law" which the old testament saints "delighted in" (i.e. Psa 119:47) was that part which pointed to God's ultimate will and is summed up in, "he that loveth another hath fulfilled the law" (Rom 13:8).
The grace Christ brought allows us to have unconditional forgiveness (through the Spirit) in loving others "as I have loved you" (John 15:12). This is what requires regeneration because it is, "A new commandment I give unto you, That ye love one another; as I have loved you, that ye also love one another" (John 13:34). This was similar but unlike the old commandment which involved conditional love, which was to love others the way you loved yourself or as yourself (Lev 19:18).
Another reason I believe Paul was referring to "the will of God" when he referenced "the law of God" is because at this time of writing, the OT law was "taken away" to "establish the second" (Heb 10:8); which is the NT or "the everlasting covenant" that is "through" His "blood" (Heb 13:20) or "in" His "blood" (Matt 26:28; Mark 14:24; Luke 22:20).
I really like your transition from Lev 19 to John 13. That is a powerful perspective beyond what I think your article spends time in.