packing with time-variant weights
I'd suggest formulating this as an instance of SAT or ILP, then using an off-the-shelf SAT or ILP solver.  This smells like the kind of problem that might be NP-hard in general and thus it might not be reasonable to expect a general, efficient algorithm that always outputs the optimal solution.

For example, if you only wanted to find a solution that meets all of the constraints, and you ignore the priorities, then you could express this as a SAT instance easily.  You could use a one-hot encoding, where the boolean variable $x_{i,j,k}$ if representative $i$ is assigned to seat $j$ in session $k$.  Then each constraint can be translated into a logical predicate on these boolean variables and thus into SAT.  I find the Z3 solver convenient for expressing these kinds of constraints.

To capture the priorities, you could introduce additional boolean variables, say $y_{i,k}$ is 1 (true) if representative $i$ changes seat after session $k$ or 0 (false) otherwise, and then add constraints to capture the relationship between the $x$'s and $y$'s, and finally minimize the sum of the $y$'s, or require that the sum of the $y$'s be below some threshold $\tau$ and use binary search on $\tau$.  For that, pseudo-boolean inequalities or integer linear programming might be useful.

There are many details that would need to be filled in. I'll let you work out the details.

See, e.g., Express boolean logic operations in zero-one integer linear programming (ILP), Encoding 1-out-of-n constraint for SAT solvers, Reduce the following problem to SAT, When to use SAT vs Constraint Satisfaction?, https://stackoverflow.com/q/43081929/781723 for some relevant reading.  The operations research community and tools (e.g., OR-Tools) might also be relevant.