Most of the major tire mfrs have good tech info on the web. Michelin is an excellent example of this.

The standard mode is to input vehicle info and then the system will output tire size. If you then look at the tech specs of the tire in that specific size you will get the outer circumference as well as the number of turns over a set standard distance. It will also show the range of rim widths that is recommended.

Once you have that data for the 'recommended' tire, print out the tech specs. You can then study other options by using the non-standard mode of selecting the tire type then the desired size and check the circumference & rim widths to find one that fits within the guidelines. You want to try to stay close to the original circumference. Costco won't install a tire that deviates more than 3% on circumference.

The speed rating of the tire is another thing to consider, and you will find that within a particular tire type, there will be different ratings for different sizes, etc.

I'm sure that your car has a 'V' rating or higher; it may be a 'Z'.

In Michelins, the Pilot A/S & Pilot Sports are really nice and they will have sizes that will fit. Pilot A/S has better wear rating than Sport and has excellent traction on a '98 SL500. I think those were 245-35-18's in the rear, it might be wider, but was a 35 series. Looks real nice on the AMG style rims.

Michelin also has great chart that shows price vs performance. It has a shape that climbs steeply then flattens out at the top (peak performance), showing how as you get to the top you can't get a lot more performance (traction) even by adding more money.

By the way, you didn't say what you don't like about the current tires. Is it the look or the ride?

With the larger AMG rims, you may have trouble increasing the height if your concern is the look. That sort of change would have a big effect on the circumference.

If its the ride you don't like, then there are options.