A bit of research suggests to me the best way to do what I want is convolve the signal to remove with the series, and subtract the signal at the peak of the convolution, if it passes the threshold.
Also found out that convolution can be calculated much more quickly than N^2 (my original concern) by using the Discrete Fourier Transform. The DFT of convolved series is the same as pointwise multiplying the DFT of each series. So, taking the inverse DFT of the pointwise multiplied series' DFTs will give me the convolution with a cost of N log N instead of N^2, if I use the Fast Fourier Transform.
Also found out that convolution can be calculated much more quickly than N^2 (my original concern) by using the Discrete Fourier Transform. The DFT of convolved series is the same as pointwise multiplying the DFT of each series. So, taking the inverse DFT of the pointwise multiplied series' DFTs will give me the convolution with a cost of N log N instead of N^2, if I use the Fast Fourier Transform.
I'll try this out and report back!