How can I hold pieces in place between turns?
Use an acrylic or polycarbonate overlay designed to fit over the game board, with fitted slots that the individual pieces fit in.

One example is an official expansion for Azul called "Crystal Mosaic."  The overlay itself is shown below:



Here is the overlay in use:



An overlay isn't going to solve every possible scenario, but in my anecdotal experience, the main thing here (which is not exclusive to long gaming sessions) is that someone accidentally jostles the board or table and pieces move.  This overlay may solve that.  Plus, it is apparently cheap enough to manufacture that the above Azul expansion is being sold for about 10 US dollars at time of writing.

This answer assumes nothing about copyrights associated with such a solution - if the plan was to market such a thing as Azul's publisher did (in 2020)