This might sound condescending and overtly simplified, but I think that Koeman can be an improvement over previous coaches by simply fielding players in their preferred positions.
First order of the day, play Messi through the middle predominantly (obviously he will roam around as he usually does but make his nominal position central). Whether as an AM or as a false nine, but none of this faux right winger crap.
On the wings, deploy actual wingers who are willing to consistently track back and help the defense. Trincao looked very promising from what little snippets I've caught from the preseason. With luck, maybe Dembele won't reinjure himself, there's Fati who's shown a lot of promise and maybe someone else arrives. By doing this, you're solving a major problem, namely that Barcelona's right flank leaks as a sieve with Messi nominally there and their right back having to more or less hold the fort alone which would be probably impossible even if he was still prime Dani Alves. This way you at least get equal coverage on both flanks, theoretically anyways, and Messi's lack of defensive contribution is least dangerous if he is in the center, especially if he is a striker/false nine.
Problem with this is obviously that you have Messi, Griezmann and Coutinho for attacking midfielder/striker positions, so obviously one needs to be on the bench, and that would be a brave decision, but one I feel is necessary. It would probably be easier and less controversial to try to shoehorn them somehow, but considering that both Griezmann and Coutinho failed to impress when played as wingers (and that's an understatement) I feel it just won't work consistently against better opposition.
Limit Busquets to easy home games. Whether Pjanić will fit alongside De Jong remains to be seen, but Busquets is more or less done at this level so he's certainly not the solution. I seem to recall that he was tried in a double pivot with Mascherano on occasion by Luis Enrique during 2014/15 and was spectacularly woeful (and that's a five years younger, miles better version of Busquets as opposed to current one).
Defense I guess he can do nothing about personnel wise, whomever they get to replace Semedo will likely be the same level at best. Just try to fix all these glaring midfield/attack issues which should at least alleviate some of the pressure.