I would invert the order of the two words and use, in preference, the term ecological-economic rather economic ecological, but I see the term as a very useful and indeed vital, one.
Something makes ecological-economic sense when it is concurrently consistent with the normal logic developed in standard economics (efficient allocation of resources to meet human needs with minimum waste), and also, meets human needs without doing any lasting damage to the major natural ecosystems of planet Earth. Functional natural ecosystems, are, fundamentally, essential to human life as much as to the viability of all living species, and are therefore a pre-condition of an enduring economic system.
So rather than pursuing the vague objective of "balancing" ecological integrity and "economic benefit", we can instead pursue the better-defined aim of maximizing cumulative ecological-economic benefit. In effect, we aim to maximize human well-being subject to a strictly-observed ecological-integrity constraint. Where a projected "economic benefit" would transgress the ecological integrity constraint, it is in effect, uneconomic in the ecological-economic sense.