until most of the way through

[GoodTaste]

The other prefatory comment that I would make is that I am going to, until most of the way through, attempt to adopt an entirely positive, rather than normative approach, and just try to think about and offer some hypotheses as to why we observe what we observe without seeing this through the kind of judgmental tendency that inevitably is connected with all our common goals of equality.
https://www.pbs.org/newshour/science/science-jan-june05-summersremarks_2-22
Source: RBSO News Hour

Does "until most of the way through" mean "in the most time that I speak here"? Just a guess, it is not clear to me.

 

[tedmc]

I think it means "for the greater part of my presentation".
"in the most time I speak here" is not grammatical.