The Over-Flowing Goodness of God versus "Common Grace"

"And from there He arose and went away to the region of Tyre and Sidon. And He entered a house and did not want anyone to know, yet He could not be hidden. But immediately a woman whose little daughter had an unclean spirit heard of Him and came and fell down at His feet. Now the woman was a Gentile, a Syrophoenician by birth. And she begged Him to cast the demon out of her daughter. And He said to her, 'Let the children be fed first, for it is not right to take the children’s bread and throw it to the dogs.' But she answered Him, 'Yes, Lord; yet even the dogs under the table eat the children’s crumbs.' And He said to her, 'For this statement you may go your way; the demon has left your daughter.' And she went home and found the child lying in bed and the demon gone."
- Mark 7:24-30

In 1924, a controversy broke into schism over the teaching of the Christian Reformed Church regarding "common grace." The CRC advocated a providential favor of God toward all, whether reprobate or elect. In opposition to this position, the minority, which eventually seceded to form the Protestant Reformed Churches, while not denying the benefits God gives to all, denied that this was properly grace, which, in their view, could only be particularly given to the elect.

Like the PRC, I am uncomfortable with referring to God's "grace" to the reprobate. Afterall, the very definition of reprobation is that God's wrath has been sovereignly determined for a particular individual, as in Romans 9:11-18. It strikes me as incongruous to refer to God's grace and sovereign wrath toward the same person.

However, I would say that God is infinitely good, whether from the perspective of the elect or of the reprobate. The difference is that God is actively good to the elect, i.e., the "children" in the story above, while His good passively overflows to the reprobate, i.e., the "dogs" in the passage. We also see this in the rain on the unjust (Matthew 5:45), and food and gladness (Acts 14:17). It is even seen in His restraining His wrath for as time (Nehemiah 9:17). I do not understand the PRC position well enough to say whether this is also their view.

Another reason I would distinguish between the grace and the goodness of God, as I have here, is because I believe that the goodness of God experienced by the reprobate actually increases His wrath against them. Think about it this way: they have experienced the goodness of the living God, yet choose to hate Him anyway. How can he not punish them all the more?