Yes COX1 & COX2 work to prevent AA from being converted to prostaglandins (not sure about LOX, although that maybe why some get and asthmatic rxn to COX's), but the two mechanisms of EPA work before COX1's or COX2's mechanism of action. EPA inhibits delta-5-desaturase (alpha-Linolenic acid to AA is blocked) and PLA2 (blocking PLA2 preventing the conversion of phospholipids to AA) after a stimulus both which are responsible for the production of AA, one step ahead of COX's.
To my knowledge Cox1 & 2 doesn't reduce the concentration of AA, it blocks AA from being converted into prostaglandins. EPA reduces the production of AA, a step ahead of COX1 & 2...both together should be an additive effect with COX1 & 2 having less AA to "fight" for convertion of AA to prostaglandins.
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