i have a 11' S4 with very very hard paint as well.
I usually go aggressive 'with the product choice' instead of bearing down extremely hard on the paint with the polisher with lighter products. Doing this will keep you from heating up the paint and having your products act finicky by flashing off early. It also helps save your pads.
I find that Meg's MF pads work very well for this technique along with D300/105 mix. basically a 75% D300 and 25% 105 mix on the pad.
If trying to remove any sort of defect usually anything under a LC Orange pad does not work. The Hydrotech cyan and tangerine pad system do work great on hard paint as well.
My polish's that work very well on my Audi for defect removal are :
D300 / 105
Menz 1500 / 2500
I also just bought some FG400 and Megs 101 but have yet to use them. So I personally would avoid recommending them myself at this point. I started machine polishing my cars in 2009. I have always had VW/Audi vehicles and when I got recommendations on Autopia forum back in the day nothing the forum suggested to me worked. So I became very discouraged (your probably feeling the same way). Back in 08/09 there werent as many quality compounds available like there are now, so not many people suggested them like they do now. So most all the meduim cut polish's that I bought did not produce results. Since then, there has been a trend of people going in head first with compounds more often then not. So many companys have followed suite and produced quality products. we now fortunately have many options for hard paint that work well, but more importantly dont scoure the finish forcing a 3 step regimin to refine the paint.
For polishing Megs 205 and Menz SF4000 are basically all I use.
To remove defects you really gonna have to go after the aggressive products to get anything done in a reasonable amount of time, just be aware of the body panel temp's. Which is why I like using very aggressive products so I can use reasonable (normal) pressure on the machines to keep everything cool and lasting long. if your only using a medium cut polish to remove defects your gonna have to use a ton of pressure to get results, which will wipe out your pads and be hard on your machine. Also the products become very unforgiving. forget 105 with that technique, it just bonds onto the paint and becomes concrete IME.