I'd say this is probably true from about 1990 on, rather than the mid-80s. During the late 80s, the Squad book featured quite a few references to his history with Batman, as well as a couple more Bat-encounters during crossovers. At one point, however, Batman basically called Deadshot on the fact that the latter had plenty of chances to kill Bats and never did, and to stop wasting both their time.
After that, I'm not sure the two ever traded blows (or shots) again, even though Batman made several more appearances. I would say that if there was a point at which Deadshot stopped being a Bat-villain, that was it. I doubt there was an official policy change; more like the writers and editors simply followed suit.
And that eyepiece looked bulky even when he had the full costume. You don't need to be a dead shot when you're wearing that contraption; they could put Mr. Magoo in the suit and get results.