This is not an answer but a tip how to change the implicit solver:
"TimeIntegration" -> {"IDA",(*"MaxDifferenceOrder"->2,*)
"ImplicitSolver" -> {"Newton", "LinearSolveMethod" -> "Pardiso"}}
Sometimes this is useful when you get a message that a matrix is singular. In version 13 this will be the default. Unfortunately, this does not solve problem at had;hand; I suspect that the PDE model is not quite correct but I can not prove it.