A 33" sink undermounts into a 33" cabinet as long as the sink is strapped, not clipped or blocked, in place, I don't care what Kohler says. Hercules Universal Sink Harness or a Sink Strap or two. I've done this a kajillion times.

You may relieve the top of the cabinet to provide room for the sink flange. The strapped sink does the top support work the relieved cabinets would have done.

Relieve the top of the cabinets about an inch. Install the straps to the cabinet walls. Set the sink flange on top of the relieved cabinet sides. Have your top installed. Silicone the sink flange, clamp the sink in place, check the reveals, tighten the straps, pull the clamp, hook up your plumbing and you're done.

If you don't want to follow the instructions above, the Kohler K-5707 Iron/Tones 33" Single Basin Enameled Cast Iron Kitchen Sink can be installed in a 33" cabinet if dropped in.

Sorry but IMO SS is the answer for a sink in a kitchen and never enammelled cast iron , there is a reason they went bye bye one chip and the thing looks like you got it from the dump. I agree you can do a drop in but Joseph is the guy when it comes to sinks .