Seems like it would be easy enough to recomposite the phaser strike in such a way that its origin point is modified. Even if the perspective was 'off' as a result (which happened a lot of the time on TNG anyway), it's not like the shot would be on the screen for more than a couple seconds.
And that's assuming the paintbrush animation effects were ever even captured on film in the first place. They may have been applied strait to video and then composited in some way. At least with models, you can make the case of using film to get the lighting texture right. But it could be that animation effects such as phaser shots would need to be recreated entirely.
Was there any additional weapons fire exchanged during the shot? Or any reverse-angle shots of the alien ship immediately before or after? Those are the only issues I can think of in regards to simply replacing the shot as you suggest. As long as the 180 rule isn't violated (as TOS-R did a couple of times!), I don't see why not.
I've never been one to notice such details where spaceships are concerned. Even now, after all the hours I've of Trek I've watched, I doubt if I could tell you 'exactly' where the phaserbanks are, especially on the D. I know a couple of phaser/tordedo effects on TOS always 'looked wrong' for some reason ('The Corbomite Maneuver' seems a likely instance), and then during the remastering project it came out that mistakes like what you've cited had been the reason. Go figure.