At risk of restarting the Great Steering Debate, let me begin by saying there is nothing wrong with a cable/pulley system if set up correctly You would be amazed at how many boats left the factory with improperly rigged cable/pulley steering.
Personally, for your 28hp motor, I would much prefer cable/pulley steering over the newer push-pull system which became industry standard in later years. It is impossible to make the push-pull system work properly on that older motor.
Both cables down same side of the boat is not an issue. Nor is helm on the left.
Improperly located pulleys are a huge issue. I’ll bet that is true in your sloppy steering case.
The type of cable drum behind the steering wheel also makes a difference. The type with a spiral groove for the cable is best. but the plain drum is ok, just not as smooth.
How about posting some pictures of your setup? A picture is worth a thousand words, as they say.
EDIT: Thanks for the pictures you posted while I was typing. Exactly what I said, it is a terrible setup.