The first hint at the solution came from the garage door opener manual, which turned out to be a useful resource to read carefully when solving these problems. That model (LiftMaster 3280) turned out to have a good self-diagnostic Flash LED capabilities, which shows up when opening the lens cover on the side that has the wires and force controls.
The problem again was that the door was reversing for no reason. Even after disconnecting the opener trolley from the door by pulling the emergency release handle, the trolley would move for a few inches then reverse back. Adjusting the force and travel limit controls had no effect. But then, looking at the flashing LED every time I press the button, I noticed 5 flashes. The diagnostic chart in the manual pointed to these 5 flashes and short motor movement as an issue with the RPM sensor!
The RPM (Rotation Per Minute) sensor is a small board surrounded by an interrupter cup that sits next to the motor shatft. It's purpose is to detect resistance against the door movement and stops the motor from working against those forces to avoid damage to the motor or to whatever is blocking the door passage. Apparently when this sensor breaks, the motor cannot travel for a long distance without reversing causing the issue I had.
Another useful resource that pointed at exactly the same issue is the LiftMaster Support website:
If you have recently replaced your garage door opener's gears, the shaft bearing kit may be interfering with a part of your RPM sensor assembly called the interrupter cup. Make sure that the wire harness is plugged back into the RPM sensor and the interrupter cup is installed and seated all the way on the motor shaft, so that the edge of the cup rotates through the RPM sensor. The RPM sensor is a small 1 inch x 1 inch electronic circuit board with a 2 pronged black sensor. If the cup is not pushed on to the end of the shaft, it can cause the symptoms described.
It's not saying directly that the RPM sensor needs to be replaced, but pointing that these are the issues causing this kind of problem.
Knowing that the RPM sensor is likely the cause for this problem, the next issue was how to replace it? Luckily it was so easy to get it, since searching for it online returned many sources and costs as low as $6: http://www.amazon.com/gp/product/B000JGLXDI/. In addition, the product reviews are also helpful in pointing to similar problems and how they were resolved.
Next comes the biggest challenge, which is how to find that sensor within the motor unit? The manual has charts for the motor assembly parts, similar to page 31 in this manual: http://www.homedepot.com/catalog/pdfImages/74/746223fe-1706-44e0-a480-fe41347a16bc.pdf, but these are somewhat hard to decrypt. Searching the web returned also some links with description, photos and even videos, but again the way these photos were taken didn't make it very clear (in the future, I am planning to put some photos and videos that hopefully would make it easier than what was there), besides different models seem to have it at different locations. After looking at these, I thought that the RPM sensor will be on the side that has the logic board and gears. After removing that side nails, I spent quite some time looking for it between gears and grease without luck. But finally, after removing the rest of the nails and cover, which was somewhat of a challenge for someone not used to opening these devices (of course remember to unplug the power before opening the unit), I found it to be on the other side, the side towards the belt and trolley, hidden behind the interrupter cup with a wire plug connected to it. By unplugging the wires and removing the cup, it was easy to remove the sensor and verify it's the piece required.
Finally, after ordering a new RPM sensor, it arrived in a few days, and once replacing it with the older one, everything worked great! A new interrupter cup also came with it, but I didn't need it, since the old one was ok. After replacing it, I needed to adjust the force and limit controls since during the diagnosis they were messed up by myself and the great garage door service technicians that visited me.