I lowered the ETC1 encoder's quality setting, so it doesn't try varying the block color so much during endpoint optimization. The DXT1 artifacts in my first experiment are definitely improved, although the overall quality is reduced. I also enabled usage of 3-color DXT1 blocks (although that was very minor).
Perhaps the right solution (that preserves quality but avoids the artifacts) is to add ETC1->DXT1 error evaluation to the ETC1 encoder, so it's aware of how much DXT1 error each ETC1 trial block color has.
Error: Max: 101, Mean: 4.036, MSE: 34.999, RMSE: 5.916, PSNR: 32.690
Error: Max: 107, Mean: 4.239, MSE: 38.930, RMSE: 6.239, PSNR: 32.228