Yep, definitely planning to read Living in God's Two Kingdoms when I have a chance.
Some of what you said is above my head (parsing Dutch Reformed terminology for one), some of it I think is equivocation downstream of our different views. But I don't see how being a Christian would fail to affect your work — either in its purpose or quality (which is what I mean by "Christian work" — still secular, but qualitatively different). I understand there is frequently a disconnect, but I see that as a failure of integrity, not a result of inherent decoupling between faith and works.
Playing devil's advocate, the dominion mandate was given to all mankind through Adam, not specifically to Christians, which makes sense of that fact that unbelievers are capable of doing good work. I also see how 1 Corinthians 3:12 is in the context of evangelistic work.