Was the Strong Man 'Bound' or Was He 'Overcome'?

In a friendly debate with a co-worker, I was prepared to slam-dunk him in a discussion of the Millennium in Revelation 20 - particularly the statement in 20:2 that Satan, in the millennium, was bound for a thousand years. I was arguing that in the Gospels, Jesus literally says that Satan has already been bound. Knowing that Jesus says this in Matthew, Mark, and in Luke, I invited him to turn to any of the passages where Jesus says that the strong man has been bound. In the New King James, Matthew 12:29 reads:

Or how can one enter a strong man’s house and plunder his goods, unless he first binds the strong man? And then he will plunder his house.

The parallel passage in Mark 3:27 reads:

No one can enter a strong man’s house and plunder his goods, unless he first binds the strong man. And then he will plunder his house.

Unfortunately for me, he chose the version in Luke 11:22, which, from v. 21, reads:

When a strong man, fully armed, guards his own palace, his goods are in peace. But when a stronger than he comes upon him and overcomes him, he takes from him all his armor in which he trusted, and divides his spoils.

One might initially be disturbed that each version varies slightly, but especially by the fact that Luke's version of the passage uses the word "overcome" instead of the word "bind."

We should be fully aware that given the doctrine of plenary verbal inspiration, we allow for the personalities of the writers to influence their recordings of Jesus' teachings. As the Chicago Statement says:

WE AFFIRM that God in His work of inspiration utilized the distinctive personalities and literary styles of the writers whom He had chosen and prepared.

What then, are we to think of the Matthew/Mark (hereafter 'MM') rendering in comparison to the Lukan rendering of the teaching? MM appears to teach that Satan has been bound, in some sort of long-term sense (which certainly, prima facie appears to serve my own Amill leanings). But Luke appears to teach that the strong man has been 'overcome,' which my debating partner believed to indicate a less 'permanent' sort of fate for the strong man (a momentary victory, as it were). Initially, I conceded that it appeared to be so, but after looking at the range of meanings, I have changed my tune.

As you may have noticed, MM have Jesus saying that the strong man has been 'bound' (Gk. 'daesae'), which is from 'deo' and is generally translated 'bind, tie,' but it is sometimes used to refer to someone's arrest or imprisonment.

Luke, however, records Jesus as saying that the strong man has been 'overcome.' The Greek word here is 'nikaesae'. The lexical form of this Greek word is 'nikao,' which is translated, in different places, as 'be victor, prevail, conquer, overcome, or vanquish.'

The solution to this seeming discrepancy is to first remain consistent in employing the perspicuity of Scripture and acknowledging that both words ('daesae' and 'nikaesae') are complimentary. The strong man has not been bound to the exclusion of his having been overcome, nor is he overcome to the exclusion of his binding; this is not an either/or situation. As such, one might understand the Gospels collectively to be conveying Christ's idea in this way:

Or how can one enter a strong man’s house and plunder his goods, unless he first binds in victory the strong man?

A similarly likely way of understanding it would be:

Or how can one enter a strong man’s house and plunder his goods, unless he first overcomes and binds the strong man?

I am, of course, only helping to solve a perceived discrepancy, not to suggest an alternate translation. This should be obvious, I hope.

In either case, if the Amill claims that Satan has been bound and then appeals to this passage in MM, it would be a mistake to attempt to turn Luke's rendering of the passage against MM. It is not either 'overcome' or 'bind,' but it is rather, both.