"But so as not to seem ungrateful I will of course defer to your greater experience." Now THAT'S eloquent Jord...
It’s one of those ‘simple’ jobs to do when it’s staring you in the face but as as usual, several ways to approach a remedy - not easy to decide best way forward from the confines of a keyboard I’m sure you’ve sorted this but your pic of the plasterboard square shows it proud of the wall surface ? It needs to actually be 2-3mm below finish surface of wall to allow a depth of filler (but I’m sure this is in hand) If your using scrim tape (?), you need to scrape off around 25mm of plaster from wall around PB square. This will allow to recess the scrim and again for depth of filler I also PVA (diluted 1-5) cut edges of plasterboard in these situations to get a good bond between filler and PB Probably not essential but makes me feel better
While visiting Homebase to collect the 5x1kg multipack of Gyproc Easifill recommended by jackelliott07, I notice a pack of these: Would it be better to forget about the batten behind the wall and just use one of these per hole instead?
Never used them before but i would be wary - you've already done the hard part, and would need filler with those patches anyway still. If you want to save a few £ you can probably get away with any general purpose filler - i only recommend Easi-fill because (in my opinion) it is far better than the majority of the competition, and sands very easily, but almost any filler will likely do the job well enough.