I looked on heatsinkusa and could only see a $12.35 option for 4" wide cut to 4" length. I guess I didn't find the right one. Can you give me a link to the $5 one? I'd like to see and if it's right then I'll just tell people they could order those, though I think even cheaper options could turn up.
I see they have a 4" wide option with 2" high fins for $12. Maybe that is large if we want to stack them close together.
They also have 3.5 and 4.2" inch sizes with .75" high fins for about $4 and $5 respectively. If 3.5x4" is big enough, $4.36 is pretty cheap.
Those 2" high heatsinks are quite beefy. The site claims a thermal resistance of 1.4 degrees C/watt for a 3"x4" section (presumably with natural convection). With such a thermal resistance, it looks like you can dissippate the heat of 16 chips with a slow/quiet fan, or perhaps no fan at all.