We get high temps and humidity in our area in the summer too, and my house has no trouble staying at 74-76 on 100+ days, but to make it feel more comfortable I do ran a fan in the den to circulate the air....that way when the A/C unit kicks off it doesn't feel stuffy. My house was built in the 60's and is not energy efficient, it still has the original windows and doors and it's a multi-level....
I have heard that 20* delta thing for years, but I agree that I think they mean the difference between the air into the plenum and the air out, cause I can't imagine getting the house comfortable if you could only get 20* below outside temps, it would NOT be comfortable if it was 80+ inside on a 100+ humid Kansas day.
As to the OP, I think the other poster is right that you've got something keeping you from getting good temp exchange from the A coil - dirt or ice on it. You can buy a chemical that you spray on the coil, it's slightly acidic but it smells nice, with the A/C off and the coil defrosted, you use a pump sprayer to coat it and let it drip off, you might have to do it several times but it will get it clean. I agree cleaning up any excessive drippings is a good idea. That and a good clean filter might be all it needs......however if it's icing up you're probably low on Freon....
Also make sure your outside coil is clean and the fan is running properly...if you can shade the outside unit it will help it too.....