The adjoint method has a much larger overhead than the forward method. Thus it’s not about what gives you the smaller number with n and p here. The CVODES manual states that adjoint is better - usually - whenever p is greater than n… it’s a matter of trying is my view.
And really: Do try to run with less accurate backwards solve. If these still give you no sampling issues, then things should run faster. Moreover, I found that the Adams solver does relatively well (which it never did for my problems when using forward).