As I mentioned in the video I ended up using the painting to test some glazing techniques. You can see it's been divided into three sections. These were all done after the painting as touch dry. From left to right, my notes were as follows. Not the most precise, but they were meant as more of a starting point.
One part titanium white to 3-4 parts liquin. Can be wiped nearly clean (compared to 3). Canvas texture smoother (compared to 3)
A bit of titanium white, couple drops of turps, and a bit of liquin, mixed to kind of a milky consistency. Tends to really sink into the canvas but smoothes fine with a brush, and ended up with the least texture. Can be wiped nearly clean (compared to 3).
Pure titanium white. Doing it with just a brush was impossible (might be possible with zinc white) so I used my thumb and that also helped reduce the canvas texture. And afterwards I wiped away the excess paint with a rag but it's hard to wipe away completely.
To avoid using turps I think the best solution would be to just prime and sand the canvas smooth so that paint doesn't get stuck in the canvas texture. With that even pure titanium white could probably be laid very thinly.