Implementation of gain scheduling for a PI controller
if you want the transition between two sets of controller parameters to be smooth, you need to apply the integral gain before the integrator. The controller output will perform a step otherwise, which is the exact opposite of seamless.

Your speaking of a PI controller and you have to apply a suitable strategy for the proportional gain too. Possible solutions are, but not limited to:


apply a 2nd order filter to the controller parameters to ensure smooth transistion, this might affect controller stability during transistion but this shouldn't be a problem with your simple control loop.
Implement a controller per parameter set, one of the controllers is active while the others are in tracking mode, switch over when another set of parameters is required. This will ensure, that the controller runs instantly with the correct parameters which typically doesn't destabilise the control loop. (Simulink PID Block, search for tracking)
Try to find a function that expresses the perfect controller parameters based on the current load situation and adjust the parameters accordingly. This might be tedious though.