What was Divine Justinia's original plan?

Cassandra explained it in DAI. The Inquisition was a backup plan for ending the Mage-Templar War. In the event that the Conclave failed to bring peace, the Inquisition would be used to subdue the Rebel Mages and Templars as well as protect the civilians from the fighting.

As the previous two posters have said, it was always Justinia's intention to use the revived Inquisition to force a resolution to the conflict between the mages and the Templars.

I think that Cassandra was correct in stating that it was never Justinia's intention to totally ditch the Circles but to bring about reform within the Circles, perhaps giving them a greater degree of autonomy then previously. It should be remembered that she authorised Pharamond's research without the safety net of Templar oversight, which would indicate she didn't exactly appreciate why their presence is sometimes beneficial to everyone involved when dabbling in dangerous experimentation. However, the fact that she was willing to force tranquillity back onto Pharamond would show that she still thought that this was the only way to deal with mages who might be in danger of possession (Pharamond having proven it was not possible to strip a mage of magical power without making them tranquil).

There didn't seem to be much evidence that she was dissatisfied with the Chantry as a whole. She certainly didn't mind using her political power to get Celene to toe the line over the elven rebellion, so I doubt she would have rededicated it to charitable works and a less political outlook. She had authorised a revised edition of the Chant of Light, including the dissonant verses by Hessarian and the Canticle of Shartan, so Leliana was following her ideas on this one. Whether she would also have opened up the priesthood to other races is less certain but whatever the case, it is pretty certain she would have used the Inquisition to enforce whatever she decided to do.

Perhaps not official oversight, but it seems from some of the notes we find in Western Approach that at least some Templars were there with him.

If the games have taught us anything though, it's that Templars are no match for demons.

He may have had some Chantry personnel along on the trip. After all we know that tranquil are not very good at defending themselves from danger so he would have needed someone to guide him to Adamant Fortress and ensure his safety on route. However, it seems highly unlikely they were actual Templars or that they even stayed once he reached his destination. The decision to seal the doors on the Keep was taken by the Lord Mayor of the settlement as a precaution should the experiment go wrong. That suggests there were no other people there who could take the decision. Certainly, if there had been Templars, then the decision how to guard against problems would have been theirs. Yet Pharamond indicates that it was the residents of Adamant who supported him in his efforts and makes no mention at all of other outsiders being there. So it seems likely that he was escorted to Adamant and then left there. After all there was no knowing how long his experiments might take and it was not the best of locations, so any outsider would wish to leave as soon as they could. 

The codex in the Western Approach is in a cave, so he may have been there conducting experiments before heading to Adamant.   Whilst the author says they will stay with him, we do not know whether that was at Adamant or not.   In fact the journal could have been left there on a return journey.  However, if they had been Templars then leaving would have been a dereliction of duty, so whoever had been with him it seems probable they were not Templars.    It is also possible that the author remained outside of the Keep when it was sealed.   After all someone had to have known that he had become possessed, unless Wynne got her information from denizens of the Fade, so may be his original escort survived and reported back what had happened.   However, if they had been Templars, I think Lambert would have known about it prior to being informed by Wynne.

One word: Politics