Using construction adhesive to connect 2 wooden panels
I would run the adhesive bead 1” from the edge and then fill in with lines or waves (shape won’t matter) about 3 or 4” apart.

When putting together I would hold the edges open by 1/8” and work out from the centre as you plan.

You could get a similar result by working from one end along the length tightening from the centre out to the sides and removing spacers as you go - centre sag won’t be an issue as long as you get reasonable clamping. Putting bricks on the surface will help but make sure the support prevents bending.