Glenn,
Here are a few things that I do and perhaps one or more of these tips can be helpful to your workflow. You are already doing most, if not all of these, but for other viewers, this may help.
The key is to move as fast as possible and keep the glue as wet as possible so that the strips can slide into place. To do this, I use Titebond Extend which delays the set time for a few minutes. I use a clamping channel made from extruded aluminum with a fixed right angle at the lower left. The channel is three sided, open at the end. It is set to be just wide enough to match the length of the strips but is not fixed as I need to be able to apply clamping pressure on it.
I dry fit the entire length of the glue-up. I then lay a 1" dowel along the entire length of the outside of the three channel elements and clamp against them. With the dowels in place, the clamps apply pressure at the middle of the thickness and lessens the chance of up or down bulging. I use no less than four clamps for the channel and set them all to the proper width and set them aside. I use two clamps for the length of the board. I use Bessey clamps.
For the glue-up I will only be applying glue to one side and this is purely to speed up the process. I start at the right and tip the last segment up and to the right and then I turn every other segment up and to the left. This keeps me from gluing the outside of the first and last strip. The block of all strips is now as far to the right of the channel as possible and I put a clamp to put slight pressure on the block to keep the glue from getting between the strips. I use a silicon roller to get an even spread on the top of all the segments.
Starting from the left, I lay the strips into their final position, but I don't let the surfaces to be glued touch yet. When they are all laid out, I quickly move them together put the clamps in place and snug. I then start in an alternating pattern, tightening each of the six clamps by one twist. If the glue is still wet, everything will slide right into place and the alignment should be perfect.
The final thing I do is add a clamping caul that I made from six 1/4" strips of oak that I bent around a gentle bend. This forces all segments to be forced flat.