You probably are getting some bass doubling when you put the sub in-line with the mains and hook it up to the LFE output, since you're getting the amplified signal from the mains' output plus the line-level input from the LFE output. (I'm not entirely sure how the signal path works in that scenario -- where the high-level input would "merge" with the internally amplified line-level signal -- but the two have to be mixing somewhere for the "two connections" method to work, probably immediately downstream of the sub's internal amp...)

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