Rodgers is shooting himself in the foot doing a couple of things. The 4-3-3 he's playing is too rigid currently. Firstly, I think it needs to translate into the 4-2-3-1 while going forward, which most of the personnel should be familiar with.I don't think Gerrard is out of his depth (although it'll be interesting to see what Rodgers will do when Lucas is back) but regardless I'd be tempted to give him a go further up the pitch along with Suarez.
As said the other day, he is the best finisher at the club and right now the whole "greater than the sum of it's parts" thing looks like it'll take time so I'd rather gamble on quality even if it is on the wane.
Gerrard playing deep has always cramped others, and I've said this so many times that I've lost count. He's best left playing up in the final third of the pitch. Contrary to popular opinion, I don't think he doesn't have the 'legs' for it anymore. If anything, it's a role which requires less kicking and rushing, less forcing the play, and more opportunities to conserve energy. The deeper he plays, the more space he cuts off for the deeper lying midfielders - and restricts their ability to influence the game with their passing.
Borini, I'm convinced, needs to play in the centre. His attributes are his movement, and his eye for goal, not his ability on the ball. A wing-forward needs to have ability on the ball first and foremost, and Borini doesn't have that. Playing him out wide on the right is therefore a moronic idea. Playing him out wide on the left is a slightly less moronic idea as the natural angle of cutting in, will give him far more opportunities to get past a player than on the right, but really, if he's not that sort of player, why play him out wide at all? Use him through the centre a'la Welbeck for United, with Gerrard right behind him. That's his strength, and his ability to play off the defence's shoulder and pull central defenders out of position will be the best use of his skillset in our attack IMO. Use Suarez and one of Sterling/Assaidi as the wing-forwards, and also Downing occasionally if required (on the right only though please). That IMO should give us a working attack for the time being, at the very least. The problem, of course, will arise when we'll need to rest one of Borini and Suarez, and I honestly don't even want to think of that scenario at the moment. I've suggested picking up Tuncay on a free, and IMO, picking up someone like him really is an absolute must in our current situation, and at least give us 'options'. Forget a finisher or a goalscorer people are claiming we lack. Not having ANYONE at all to play in an attacking position is a pretty disastrous scenario, and it's why we really do need to consider every free agent option available (barring the cunt).
As for central midfield, between Allen, Sahin, Henderson, and Shelvey we should be well covered. But I'll re-iterate that it'll be critical for our attack to be functional to let the midfield two have sufficient space, and that necessitates shifting to a 2-3-1 formation for the front six. Rodgers 'insistence on a 3-3 formation may be borne out of his desire to have two banks of three pressing high to win back possession immediately (which is presumably what Barca do, I'm not sure - I barely watch them play, you should be able to correct me on that) but I don't see why reverting to something like that once we lose possession isn't possible. Ryan made the point some time back about the likes of Shelvey needing space to be effective. Sahin isn't dissimilar. He's a quality player, who's wonderful in possession and can pass superbly, but given that any sort of single-point playmaking in midfield requires you to indulge in a more expansive range of passing (which perhaps is not entirely Rodgers' plan - he probably wants a front six of equally skilled technicians all on the same wavelength and playing close to each other, as opposed to a single player or a two-man midfield setting the tempo - but as you say, given that that's not the case currently, he HAS to adapt), it necessitates ensuring that that single-point is given sufficient space in midfield. Playing Gerrard deep denies that player that, and also highlights Gerrard's less impressive qualities.
Lucas coming back in November-December should also give us a filip. I've never been his biggest fan, but he'll give us fresh options tactically, including the ability to push Allen in the final third (which, I have the hunch, could eventually prove to be his long term position), and even try Gerrard in the false nine position.
But, as you very rightly said, Rodgers needs to focus not just on the long-term but on the short-term as well. It is, as the cliched saying goes, a result-oriented job, and he'll have to be very clever with the resources he's got. If he can manage to do some of the things I've listed, I do believe we'll be able to do better than the complete disaster some people are predicting. It's a massive massive test, and I'll be keen to see what he does.