EGR isn't active at idle. Deleting EGR isn't going to cause problems at idle, 'cause it wouldn't be working anyway. Something else is wrong.
Eye-watering exhaust is almost always a misfire problem. Connect a scan tool, look at codes, but more important, look at the data stream. If this is '96+, you'll want to pay particular attention to the cylinder misfire counts.
Once you know which cylinder(s) are misfiring, you can check them for compression, vacuum leaks, fueling or spark problems.
And, of course, your catalyst is probably ruined.
Deleting EGR is borderline crazy. EGR is not hurting anything, doesn't rob power at heavy throttle. Has the theoretical ability to improve fuel economy (but not by much.) The only actual complaint is that it makes the inside of the intake manifold "dirty", which is only a problem in extreme cases.