First things first, if your car had a fully choked exhaust, there is not way its mileage is actually 82k. It should be more then twice that much or so AND it has to be run on the most pathetic fuel available. If the car was ever used on CNG, the cat should be okay as CNG does not harm it. anyways, coming to the problem.
When the CAT is removed, the exhaust sensors get wrong readings. They see materials in exhaust gasses which should not be there and assume that the intake air is not of good quality and hence they change the fuel injection settings and may also tweak the timing of the ignition. But since the air coming in has nothing wrong with it, these changes act negatively on the performance and make the car worse then it would be without the sensor's input. I think the engine is turning the air-fuel mixture lean and is advancing the timing due to which the engine is knocking and when a/c is on, the impact worsens as the engine is under load. I cannot be 100% sure but that is what seems to be happening.
I am assuming that the car runs fine without a/c? i mean the performance is fine. if so, then Honda guys are trying to rip you off by saying that rods need to be replaced. If the rods were bent, you won't be able to drive the car pretty much at all. n other then bending, theres not much that can happen to the rods. Also, if the clutch plate was gone, the car would drive bad all the times. The symptoms of it could be similar but they are two seperate things.
The sound could be coming due to two reasons, knocking being the first. The second is that your CAT acts as a sound damper too, with it gone, the sound of engine's cycles will be more audible.
Anyways, try high octane, if the noise reduces, it certainly is knocking.