AKA give me a trendline than handles periodic noise

Like a lot of people who menstruate, my weight fluctuates naturally in semi-regular cycles. Beeminder has really fancy graphs, but it seems like all of the smoothing tools are designed to handle random noise but not periodic, correlated noise. It would be nice if one of these tools (moving average, polynomial fit, optimistic projection) were capable of taking into account the sine wave and showing me the real trend.

For example, every time I enter the peak of the cycle, the optimistic projection freaks out and flattens a lot of my past progress. It's not clear to me at all why the optimistic projection is so sensitive to the upswing. On the other hand, whenever I enter the trough of the cycle, the optimistic projection assumes all the progress is real and swings equally violently in the opposite direction.

Maybe the optimistic projection isn't the most reliable way to measure my progress, but unfortunately the moving average and the polynomial fit are equally susceptible. Maybe with enough cycles the polynomial fit will eventually ignore the periodic signal (is there a maximum order?), but three months in it is definitely still over-fitting the data.

I think a lot of people find the moving average to be motivating because it helps them see the trend through the noise. For me the trendlines are mostly showing me noise and it's extremely demotivating. Right now, I have no idea whether or not I'm on the right track. Is the DC component of my signal decreasing, or am I being lulled into akratic complacency on every down-swing?