One relatively tedious (but simple) solution would be to split the large database into smaller databases, convert to smaller databases, and then recombine them.
This gives an additional advantage: if for some reason the text is an invalid date in one chunk, it will be easier to find (due to the smaller size of the chunk).
Assuming you have some kind of integer key in a table that ranges from 1 to (say) 10,000,000, you can just make queries like
SELECT * INTO newTable1 FROM yourtable WHERE yourkey >= 0 AND yourkey < 1000000 SELECT * INTO newTable2 FROM yourtable WHERE yourkey >= 1000000 AND yourkey < 2000000
etc.
Be sure to enter and execute these queries separately, as Access seems to give you a syntax error if you try to run more than one at a time.
If your keys are something else, you can do the same, but you will have to be a little more complicated with WHERE clauses.
Of course, the last thing to consider if you can use it is to switch to another database, which has a bit more features. I assume that you have reasons why this is not easy, but with the amount of data that you are talking about, you are likely to run into other problems, and continue to use Access.
EDIT
Since you still have some problems, here are some details in the hope that you will see what I have not described well enough before:
Here you can see that I created the "OutputIDrive" table, similar to the one you are describing. I have an identification tag, although I only have three entries. 
Here I created a query, went into SQL mode and entered the appropriate SQL statement. In my case, because my request only captures the values> = 0 and <2, we just get one row ... one that has ID = 1. 
When I press the start button, I get a popup that tells / warns me what is about to happen ... this puts the row in a new table. This is good ... this is what we are looking for. I click OK. 
Now our new table is created, and when I click on it, we see that our one row of data with ID = 1 has been copied to this new table.

Now you can change the table name and numeric values in the SQL query and run it again.
Hope this helps you with what's confusing you.
EDIT 2:
Yeah! This is a trick. You must enter and run SQL statements one at a time in Access. If you try to insert several statements and run them, you will get this error. So, start the first one, then erase it, start the second one, etc., and everything will be all right. I think it will be done! I edited the above to make this clearer.