I'm wondering if a cooler in tower-style might not still be better performance, even if it has to be really small compared to a large top-flow cooler like NH-C14S?
About tower-style, there's Noctua NH-U9S and NH-D9L. Those two are tower coolers in a 92mm fan size, making them short enough to fit into your 130mm height requirement. The NH-U9S is the larger one and is 125mm height and five heat-pipes. The NH-D9L is really short, just 110mm. It is dual-tower with a single fan in the middle that's mounted very low, it's four heat-pipes.
There's a new cooler "Thermalright Silver Arrow 130". It's a dual-tower cooler with exactly 130mm height in its specifications. It uses a 120mm sized fan and has six heat-pipes. I'm guessing it's the strongest air cooling that's possible for 130mm height. I can see it available on amazon.com for $80.