1991 Chevy Corvette Rough idle

Engine Mechanical problem
1991 Chevy Corvette V8 Two Wheel Drive Automatic

Recently the Service Engine light started coming on when I reached speeds of 55 or 60 Mph for about a mile. When I killed the engine for about a min. And restarted; the light did not come back on as long as I drove at a slower speed. On one occasion I had to continue driving at a slower speed with the light still on and noticed fine smoke coming from the catalytic converter on the passenger side. The shop where I took it changed some fuel injectors, plugs and wires with no change. I then cleaned out the converters but it still idles rough. My question is could this problem possibly be solved by replacing both converters? Can hollowed-out converters cause such a problem? The mech. Used the analyser but was unable to do so when the light was on. Thanks for your help.