In my view, the fact that Jesus called him "Father" rather than "Jehovah" doesn't really say much. Like others explained, the relationship being known, you would know exactly who Jesus was referring to when he said "father". In the same tone, using the name back then, again as many have pointed, was necessary due to the number of other Gods people had in those days. Nowadays, not only is this the most well known God (specially if you live in the western side of the planet) but also there are other religions that have began to adopt the name and therefore calling him Jehovah does not immediately isolate you from the rest anymore.
Where JWs fail is in understanding the analogy of uniqueness that God seeks. Is like saying Elvis was your best friend or would be if he was alive, just because you know his name and use it. With so many Elvis impersonators around, would you be able to pinpoint exactly who you refer to by using only his name? Or do you need to show other evidence that makes him unique?
If JWs grasped that concept, they would realize that is more important to say "our God" than it is to say "Jehovah" or even never use the generic term "God". It would be like naming your dog "Dog"