Apart from the time series approaches-

Fit model can be used with an overall trend data as a fcn of time, (maybe time^2)

With the strong overall trend defined, you can find a function for the overall (linear, polynomial etc) using fit model, then "save residuals"- and examine the residuals by month independent of the trend.

I have seen approaches (sometimes used when time series are not regular steps), of calculating the "phase" of the year in radians (month / 6 * pi), calculating a SIN and COS of this phase, and adding them as terms in the fit model.

regards-