Catalytic Converter Problem?

I know you might not want to hear this, but if your exhaust is stinky with a high-lift cam of less than 250*@.050 (the biggest I have tuned) then, IMO, the tune is off. Depending on when it is stinky, it could be the T-port synchronization, and or the timing, and or the fueling.
At 65=3050@ zero-slip, perhaps 3150 on the tach, your iron headed 360 will be wanting at least 50 to 56 degrees of timing. An alloy headed 360 might be asking for up to 60*
If you do not provide the lead, the fuel-charge may not finish burning in the chamber. With "late timing" the potential for max pressure does not occur. Instead, the expanding gasses chase after the piston, on the power-stroke, putting heat into the cooling system thru the cylinder walls. This destroys scavenging, and may drive hot exhaust up into the intake instead. The Mopar 292/292/108 for instance, has 76* of overlap. That is a lot of time for both valves to be open at the top of the exhaust stroke. By 3000rpm, the expanding gasses should NOT be wanting to go up into the plenum, especially not with headers. But the exhaust valves will not be "closed " until perhaps 30* ATDC, so who knows what goes on with late ignition timing. With log-manifolds, and late timing, anything can happen.
But you know, I had a 223/230/110 cam , a hi-lift .538/.549 cam in my 360 for several years. That I ran at 60=2680 with 27" tires (manual trans). At cruise, it liked 60*of timing advance with alloy heads. I could not get that out of the factory distributor, on top of the Power-timing, so I bought a stand-alone, dash-mounted, dial back, timing delay box to make up the difference.
What I'm suggesting, is that if you clean up your cruise-exhaust, your Cats may be going along for a free-ride..... at cruise at least.