So when are you thinking the 70 weeks ended then?
It ended on the day of Pentecost.
While it may not be directly stated as "annihilation" I think to "finish the transgression" is directly related to the final demise of apostate Israel in the war of AD 66-70 AD who were transgressing the Law which included persecution of the 1st century church.
Transgression means sin, not wrath or punishment... People are punished for transgressions. Finish the transgression means to finish killing all the prophets with Jesus being "That Prophet", or the final prophet.
Also you need to factor in the passing of the OT and the temple representing the things that could be shaken with the things that cannot be shaken:
(Heb 12:27 And this word, Yet once more, signifieth the removing of those things that are shaken, as of things that are made, that those things which cannot be shaken may remain.)
This is part of the 70 weeks. The bringing in of everlasting righteousness was only fully completed when the righteousness according to the Law was destroyed when the old covenant finally waxed old and became obsolete in it's vanishing away:
(Heb 8:13 In that he saith, A new covenant, he hath made the first old. Now that which decayeth and waxeth old is ready to vanish away).
The shaking of the old was still to come when Hebrews was written and is related to the destruction of the temple/law system in the AD 66 war.
I see your point on this part because of the language, but that's not enough to override all the other things that point to the 70 weeks being completed when Jesus sat on the throne of glory. Besides that, we know that the verses below started immediately while Christ was still alive or at the very least, right after his resurrection. I mean think about Paul's conversion. People didn't have to wait until 70 AD to become Christians.
Heb 8:10 For this is the covenant that I will make with the house of Israel after those days, saith the Lord; I will put my laws into their mind, and write them in their hearts: and I will be to them a God, and they shall be to me a people:
Heb 8:11 And they shall not teach every man his neighbour, and every man his brother, saying, Know the Lord: for all shall know me, from the least to the greatest.
Heb 8:12 For I will be merciful to their unrighteousness, and their sins and their iniquities will I remember no more.