07 Mazda 3, 97K miles, 2.3 L (no turbo), 5 speed manual.

I was getting code PO126 after longer drives.  Changed the thermostat (aftermarket part), refilled coolant, and tried to bleed system.  This car does not have a radiator cap- it uses the coolant reservoir for all filling and bleeding of air.  Mazda forums online recommend idling the car with the reservoir cap off until it reaches operating temperature, then revving the engine for 2-3 mins at 2,500 RPM, idle, 5 seconds at 3,000 RPM, and repeat twice to bleed the system.

Tried this and also letting the car idle with cap off for 30+ minutes, twice.  I can't seem to get all of the air out of the system!  I see air and hear air bubbles coming from lines attached to the reservoir, but they are few and far between now after trying to bleed it multiple times.  The temperature gauge is right where it should be, heat works at idle and higher RPMS, but the cooling fan goes crazy at idle and around town!  Winds up to its highest speed at times. (Usually this fan will only kick in at idle on hotter days, or if the A/C is on). My thought it that there is still air in the system, so the coolant isn't as effective, and the fan must kick in the compensate.  Unless there could be a leak where air is getting in? How do I properly bleed this system and/or find a leak?

The car seems to warm up faster with the new thermostat, and the heat is stronger now as well.  

Any ideas/help would be greatly appreciated.  Thank you!!