You are starting from three incorrect postulates:
- Scribes are just copyists, not interpreters of the law.
- The doctrine of preservation of scripture is the same as inerrancy.
- Variants have semantic importance
All three of those need to be true for your statement to make sense. Unfortunately, none of them are.
1. Scribes aren't just secretaries. They are teachers, who in this case, were corrupt
In context, Jeremiah 8 is clearly inveighing against "false" teachers of the law. This a common theme throughout the Old Testament generally, and the prophets specifically. (It is also picked up in the New Testament for that matter - Jesus seems to be more annoyed with "religious" teachers than with sinners.)
The text says:
“‘How can you say, “We are wise,
for we have the law of the Lord,”
when actually the lying pen of the scribes
has handled it falsely?
9 The wise will be put to shame;
they will be dismayed and trapped.
Since they have rejected the word of the Lord,
what kind of wisdom do they have?
Note the antecedent of "they" is those who are saying "We are wise, for we have the law of the Lord." Notice these same people are being said to have rejected the word of the Lord.
This is very common throughout the OT - those who are claiming to speak for God but are not. Malachi calls them out, Amos calls them out, and Jeremiah calls them out. It was a recurring theme.
Note that scribes are not just writers of the law - they are teachers too. Especially at this time, there was a hefty oral tradition of interpretation that had added much to the Torah.
In the New Testament, Jesus makes the same charge (Matthew 23):
13 “Woe to you, teachers of the law and Pharisees, you hypocrites! You shut the door of the kingdom of heaven in people’s faces. You yourselves do not enter, nor will you let those enter who are trying to.  [b]
15 “Woe to you, teachers of the law and Pharisees, you hypocrites! You travel over land and sea to win a single convert, and when you have succeeded, you make them twice as much a child of hell as you are.
16 “Woe to you, blind guides! You say, ‘If anyone swears by the temple, it means nothing; but anyone who swears by the gold of the temple is bound by that oath.’ 17 You blind fools! Which is greater: the gold, or the temple that makes the gold sacred? 18 You also say, ‘If anyone swears by the altar, it means nothing; but anyone who swears by the gift on the altar is bound by that oath.’ 19 You blind men! Which is greater: the gift, or the altar that makes the gift sacred? 20 Therefore, anyone who swears by the altar swears by it and by everything on it. 21 And anyone who swears by the temple swears by it and by the one who dwells in it. 22 And anyone who swears by heaven swears by God’s throne and by the one who sits on it.
23 “Woe to you, teachers of the law and Pharisees, you hypocrites! You give a tenth of your spices—mint, dill and cumin. But you have neglected the more important matters of the law—justice, mercy and faithfulness. You should have practiced the latter, without neglecting the former. 24 You blind guides! You strain out a gnat but swallow a camel.
Note: Some translations will even say "scribes and Pharisees" rather than "teachers of the Law and Pharisees." The King James, for example, says:
13 But woe unto you, scribes and Pharisees, hypocrites! for ye shut up the kingdom of heaven against men: for ye neither go in yourselves, neither suffer ye them that are entering to go in.
14 Woe unto you, scribes and Pharisees, hypocrites! for ye devour widows' houses, and for a pretence make long prayer: therefore ye shall receive the greater damnation.
A scribe was also a teacher of the law. More modern translations clarify that aspect of the culture we no longer have.
It isn't the pen, it is the oral additions.
2. Preservation of Scripture != Inerrancy
There is a wide spectrum of belief about how literally one takes the Bible.
The Ezekiel verse you quote is pretty clearly metaphor, for example, clearly written as such. The Divine moment preserved, however, is the vision of a God who is restoring Israel. Ezekiel is dealing with a people who have "forgotten" the law, in that they have chased other gods. The idea of adultery to which the metaphor alludes captures very well both the problem and the divine response.
Preservation of Scripture says only that God communicates his Law to all men. It doesn't depend on the mechanism. Even if you could find somebody who tried to misprint the Bible, the doctrine of Preservation says that the transmission isn't the point anyway.
3. We know the "variants" in Scripture, and trust me, they are a lot less "variant" than you think.
It is true that there are over 5000 manuscript fragments from which we arrive at what we believe the "Scriptures" to be. You can see these variations yourself by consulting a biblical apparatus. It is true that prior to the invention of the printing press in 1453, documents were copied by hand. It is also true that minor variations existed as a result.
It also should be understood that when the Dead Sea Scrolls were rediscovered in 1947, we found out how very, very small the differences were. Great care was taken to preserve the manuscripts.
In seminary, it was stated that no major doctrine hinges on a variant. Many Christians would argue there are no significant differences when it comes to doctrine.
Finally, Mark Twain probably said it best:
It ain't those parts of the Bible that I can't understand that bother me, it is the parts that I do understand.
Read the whole thing and you'll see there is no "conspiracy," there is no "power grab." There is a reason people have been following this book for thousands of years. It does a pretty good job of conveying who these people think God is. Food for thought.