This challenge is not unique. Especially with super small chips that aren't deep, and where the touch up repair is higher than the surrounding paint. 
Try this before you paint: You can thin the paint with up to 20% distilled water. It will flow better and be thinner in a very small and shallow chip or scratch. And you can thin the clear coat by up to 10% the same way, to get it to flow better and be a thinner layer.
Another trick: try to find a super soft artist paint brush that will allow you to apply less pressure on the paint and clear, so you can put it on even thinner. Sometimes, the stiffer the brush, the more paint you end up applying, because you try to avoid drag marks the brush leaves.
We recommend you try using the block method in the article below to provide a completely flat surface to polish with. And you won't need much pressure at all.
Note: our entire system is waterborne, so you can easily clean the brush with warm water after painting primer, paint or clear coat.

Our polishing compound is less abrasive than most. It is not a "cutting" compound, so it may work better than something you have on hand that is more abrasive. For example, Maguires has some very abrasive compounds depending on the particular product you have.
You can see a good comparison of different compounds in the link below...ours is in the middle of the range: