I think what Deks means is that Graves' transfer would work with a blank positronic matrix, even if it didn't fully work with the E-D computer (which is not positronic). However, at the time (and even by the end of TNG), no-one was able to create a stable positronic brain other than Soong (though the EMH did have some positronic components). In fact, Soong's "synaptic scanning technique" used to create android Juliana might actually BE Graves' method!
However, the fact that in DS9 Bareil had half of his brain replaced with positronic components but "replacing the other half would be the same as killing him" might be read as "we still can't maintain the personality even if we can copy the memories".
DS9 is not too reliable source because a LOT of the technology UFP used was dumbed down as the series went on for 'drama effect'.
But also, Bashir wasn't entirely wrong... if you just replaced half of his brain with a positronic component without trying to transfer his mind into it, then yes, what was left of Bareil wouldn't be him.
With half his brain already dead, he was already a goner - it was no longer him at that state... or at least a good portion of him was gone already with half his brain gone.
If they tried replacing his brain while it was still in his healthy state by transferring his consciousness into a positronic matrix first, then that might have been different... but Bashir wasn't at that stage when he started the treatments (and the outlook was initially good)... it was the psychological strain from dealing with Kai Winn and advising her that pushed Bareil into his perilous condition which resulted in half his brain dying.
Also, the technology for mind-transfer was already there... considering the fact that Bashir and O'Brien went into the mind of that dying Section 31 operative (forgot his name) to find a cure for Odo.
So, the technology to transfer the consciousness wasn't the problem... finding a suitable place to keep the consciousness from degrading was (and I suspect a holographic matrix like the one Zimmerman created and the one the ENT-D made in the case of Moriarty would have done the job - its just no one necessarily THOUGHT of doing it - Bashir was knowledgeable, but its also possible he never read the reports about Moriarty and didn't even consider using an EMH before Zimmerman paid him a visit on Ds9).
As for Ira Graves... What I meant was that his mind-transfer DID work initially... the problem was when he did it, he transferred himself into Data, which also suppressed Data's own personality.
It could have created a psychological strain which Ira wasn't accustomed to because perhaps on some level he had to supress Data's personality (similar to what happened when Kes was possessed by Tieran... he had to devote a lot of mental effort to keep himself dominant... and he was losing).
Ira Graves also had 0 emotional support after the transition and had an excessive personality which resulted in him manifesting feelings of rage and jelaousy which he didn't know how to properly control while using Data's android body and abilities (possibly because Data himself was incapable of emotion at the time and it was a new body experience for Ira Graves... the combination of both could have created a problem for Ira - but its possible this would have been manageable if he actually transferred his consciousness into a brand new Android body instead which had no personality to begin with but was an empty vessel to be occupied by a consciousness and also had some counselling support to help him with the transition).
But yes, transferring himself eventually into ENT-D resulted only in his knowledge remaining... his consciousness on the other hand did not survive that process.
Maybe if he tried a hologram instead? But this was before Moriarty's creation, so the ENT-D crew might not have known that particular option could have been viable in the first place.
Otherwise, UFP could effectively allow people mind-transfers from a biological body into say a holographic one without even needing an android body (with limitation to areas that support holo emitters - and in the 24th century, those would be plenty - stations, ships, holodecks, being transmitted instantly from say Earth to anywhere else in UFP space or beyond using the MIDAS array).
The Doctor did it with Denara Pel in the Delta Quadrant after all - but that was a temporary measure which still depended on her biological body somewhat because there was no intent on keeping her in a holographic form permanently (and he used a standard hologram no less which he made from scratch using verbal computer interface).