Yeah, that looks like the fans mount slightly differently from the one I have. Still, concept is the same.
Check the motherboard documentation and forums to see if the motherboard disables fans below certain speeds...might be what's happening. If the fans are PWM (4-pin) then check the setting for this in the motherboard menus. Not sure exactly where it would be, but it might be the source of the issue. If they're 3-pin, do the same for voltage control with the motherboard.
If none of that looks like it's the source of the issue, replace the fan.
As for push-pull, the temperature differences aren't going to be huge - I did it just because I could, and I OC. Seeing as you don't, there may be no point. However, if you do, just remove the exhaust fan. The flow from the closest CPU fan will cause air to exhaust anyway (although perhaps not as efficiently). You could also mount the exhaust fan external to the case and put a guard on it to prevent fingers getting nipped. But I'm going off-topic now.
![Wink ;) ;)](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)