(Update: The title of this entry turns out to be wrong. See addendum.)
After putting optics in the tip-tilts and very roughly balancing, the BOSEM flags looked very high, probably between 1.5mm and 2mm even though the blades were brought all the way down. See the first and second picture, note that the table is not level in these pictures, but it's obvioius that the mirror is too high.
Bram pointed out over the phone that the wire clamps should be under the blades, not the other way round. And sure enough, our clamps were sitting on top of the blades on both of two pre-assembled tip-tilts. In the third picture you can see that the clamp is on the wrong side and that the left blade adjustment is already bottoming out (tension screw is too long).
If the clamps move to the correct side of the blades the mirror height will be OK (though the blades should be set as low as possible).
It seems as if the wire length is about right (Alexa measured the height difference of the blade clamp and the mirror clamp, and it was about 140mm).
Problem is, there might be no way to move the clamps from one side to the other without compromising the wire direction. I'm asking Bram the best way to proceed.
Addendum: Now Bram says that the clamps are OK, they're supposed to be on top of the blades!
He looked up some document and it turned out that the clamps are supposed to be on top.
He suggested to bring the blade down further by using washers for the blade angle adjustment screws.
I did face this misalignment in some of the tiptilts that I assembled and in all cases could solve the problem by swapping out the blade height adjustment screws for shorter ones (allowing us to lower the blade tips further). I have attached the original design document here and some annotated pics to help you with the adjustments. Essentially there are three things which could make the flags go too high: 1) the suspension points are high 2) the backplane on which all the BOSEMS are mounted has slid down within the play in the mounting screws 3) the optic is pitched too far face-down, raising the tips of the flags inside the BOSEMS. You might be facing an unfortunate co-incidence of all three at the same time.