Were any Jedi actually successful at remaining completely emotionally unattached?

Yes, several of them.

We are shown by the movies, and so used to it, Jedi's with emotional connection. Luke has failed, Anakin has failed, but as it goes we see that this emotional instability comes with the Skywallker family. Almost every other Jedi has a strong control of his/hers emotions. Master Windu, Obi-Wan, Master Yoda. All of the them had their time of anger (as Mace Windu did when facing Palpatine, or Obi-Wan in Revenge of the Sith, fighting Anakin: "I loved you, Akakin"). But along the series they are stated as cold Jedi knights.

And these moments of emotion shouldn't be seen as rule being broken, but as a constant state that they must control their feelings, because as the Sith Code states, emotions are the path the dark side:

Peace is a lie, there is only passion. Through passion, I gain strength. Through strength, I gain power. Through power, I gain victory. Through victory, my chains are broken. The Force shall free me.

Possibly yes, but due to the idea of philosophical debate or the notion of evolution of a philosophy, and an unclear event history with no Jedi origin story in the new cannon, may have to be left as "inconclusive".

ANAKIN (to Padme`): Attachment is forbidden. Possession is forbidden. Compassion, which I would define as unconditional love, is essential to a Jedi's life. So you might say, that we are encouraged to love.

At the time of the prequel trilogy we may conclude that viewers see an evolution to the original Jedi philosophy, as Obi-Wan even tells Anakin (AotC) about his lightsaber, "This weapon is your life!", showing an attachment to a possession.

We also know that the Jedi fail in this era due to several factors such as being clouded by the dark side, as the temple on Couresant was built on top of a Sith Shrine, having a hierarchy with the Jedi Council, serving the Republic to the point of becoming "soldiers", and fears about Anakin Skywalker. Even the concept of training, mentoring, and being responsible for Padawans and younglings shows a regard for attachment.

So there could be a debate if the reason they failed was because they were not entirely selfless, if a person can truly be selfless without being selfish (ie: caring for others), and/or how strict the philosophy was originally intended to be.

However, to better delve more into your question, there were a splinter group of Jedi that may have tried to better practice the original Jedi philosophy. They were called Ordu Aspectu.

The Ordu Aspectu was a splinter group of the Jedi Order that was thought to have existed long before the Galactic Civil War, until they met their doom at the hands of the orthodox Jedi. Various accounts said their headquarters were located in the Citadel of Rur, and one of their leading members was Rur.

According to one account, supported by the father of the archaeologist Aphra, the Ordu Aspectu was a violence-loathing Jedi sect that sought to selflessly prolong life for all. When the orthodox Jedi raided their fortress, the Ordu Aspectu were forced to activate a device that seemingly caused them to disappear, perhaps ascending to a higher form of existence. However, according to the younger Aphra, another version of probable events was that the Ordu Aspectu had kidnapped Jedi Padawan learners, whom they callously sacrificed in an attempt to gain the immortality they sought. Aphra also stated that the Ordu Aspectu might not have existed at all, and the term might simply have been an argument between Jedi grammarians of more recent years.

Doctor Aphra canon comic series has introduced this sect of Jedi. As one can see, there is even a debate about the true nature of Jedi and "sects" of Jedi with an unclear history. This comic eventually crosses over with Star Wars Comic, as Aphra and Luke team-up during The Screaming Citadel, where Rur, the leader of Ordu Aspectu has created an eternal version of himself using a crystal and a computer to "project" himself. One could argue that this may be a "fake" way to appear as a force ghost, proving Aphra's beliefs about this sect correct and proving the mainstream Jedi morally better people due to compassion.