As soon as the 69th week was finished Messiah was cut off. I don't see what you are talking about in this. Messiah was cut off (crucified) as soon as the 69th week was completed.
So if the Messiah was crucified 'after' the 69th week and it was soon after (although I don't see where it says 'soon' after) then He was crucified in the following week, the 70th week. The new covenant took effect when He died and was resurrected, in the 70th week. But we know that scripture says that it began with the preaching of John the Baptist. We know that Jesus' ministry lasted 3.5 years, He was crucified, the apostles preached only to the Jews another 3.5 years and then Stephen was stoned (Saul/Paul was present) and after this the Gospel was taken to the Gentiles by Paul.
That being the 70th week.
Verse 24, tells us that there are 70wks determined for Daniels people (the Jews) and for six things to happen. I see that all these things did happen during those 70 wks., specifically the Messiah's ministry and death and resurrection. I will take the list from Adam Clarke's Commentary because I believe he has done well in explaining clearly and easily understood.
In
Daniel 9:24 there are six events mentioned which should be the consequences of the incarnation of our Lord: -
I. To finish (לכלא lechalle, to restrain), the transgression which was effected by the preaching of the Gospel, and pouring out of the Holy Ghost among men.
II. To make an end of sins; rather ולהתם חטאות ulehathem chataoth, "to make an end of sin-offerings," which our Lord did when he offered his spotless soul and body on the cross once for all.
III. To make reconciliation (ולכפר ulechapper, "to make atonement or expiation") for iniquity; which he did by the once offering up of himself.
IV. To bring in everlasting righteousness, צדק עלמים tsedek olamim, that is, "the righteousness, or righteous One, of ages;" that person who had been the object of the faith of mankind, and the subject of the predictions of the prophets through all the ages of the world.
V. To seal up (ולחתם velachtom, "to finish or complete") the vision and prophecy; that is, to put an end to the necessity of any farther revelations, by completing the canon of Scripture, and fulfilling the prophecies which related to his person, sacrifice, and the glory that should follow.
VI. And to anoint the Most Holy, קדש קדשים kodesh kodashim, "the Holy of holies." משיח mashach, to anoint, (from which comes משיח mashiach, the Messiah, the anointed one), signifies in general, to consecrate or appoint to some special office. Here it means the consecration or appointment of our blessed Lord, the Holy One of Israel, to be the Prophet, Priest, and King of mankind.
http://biblehub.com/commentaries/clarke/daniel/9.htm