Manually Beamforming 6-channel Audio (Logic Check)

I've got audio recorder from a small, 6-channel circular array (this one) and I'm after beamforming the recordings so that signal coming from the top side of the array is amplified.

I've calculated the time delay between the signal hitting the closest two mics (0cm,t=0), and the next two (4cm, t = 0.0001206), and the final two (8cm,t=0.00024133). The audio is sampled at 16kHz, so I make that ~2 samples difference between the first and second row, and ~4 samples difference between the first and last row.

I've tried cutting samples from the start of each channel (two from ch3 and ch6, four from ch5 and ch4) and then summating (and normalising (/6)) all channels in the hope of making one nicely beamformed channel. But it doesn't seem like it's doing anything to the audio's directionality. (I'm testing it on a recording where a tone is being played at different positions around the array)

Does this logic seem sound? Is the issue to do with me rounding up how many samples to remove? Or something else?