They could half-way acknowledge A3 as what actually happened mixed with altered memories.
Let's say that mercenaries were hired by Burke to board the Sulaco all along. The mercs board the ship while Rip & Co are in cryo sleep. The mercs enter the cryo tube area and start to awaken Rip & Co, starting with Hicks & Newt. But before they have the chance to awaken Ripley, the mercs are attacked by facehuggers. Fire alarm goes off and Ripley's and Bishop's tubes are ejected.
Hicks & Newt are transported onboard the mercenary ship and leave as the acid from the killed Facehuggers starts eating through the hull.
Ripley ends up on Fiorina 161, but without Hicks & Newt. Everything that happened in A3 happened except for the morgue scene, the funeral scene and Ripley's sacrifice - all that are altered memories.
In reality the funeral was for two dead inmates, the dissection was not on Newt but on a mystically dead ox. Ripley did run into a W-Y executive and his Special Ops team, but in reality it wasn't Bishop, and was caught before she had the time to commit suicide.
W-Y keeps Ripley (who is officially reported as dead) on ice. They harvest the queen embryo inside of her. Despite the comatose Ripley still shows life signs and they decide to stitch her up and stove her away. They use mind altering drugs and technologies (similar to the stuff in PROM) to extract as much information from her as possible, and since she survived the embryo surgery she is also of medical interest. W-Y perform experiments on Ripley, imprisoned in here altered state. She dreams, or more like patches together what happens to her, which is A:R.
The merc ship with Hicks & Newt on board is intercepted by the authorities. Burke is single-handedly blamed for everything that happened, W-Y gets of scott-free, Newt is sent to an orphanage or foster family (closely observed by W-Y of course), and Hicks is kicked out of the marine core and has to serve a few years in prison for whatever BS reason.
FFW a few years and there we go - A5.
They don't have to show flashbacks from A:R and A3. It could just be mentioned and hinted at, or even display it as abstract and blurry soundscapes, close-ups etc.
The opening scene could be the space station that a drunken and haggard older Hicks works at as a janitor or security guard a la OUTLAND.
Still sucks, I know. But I think it's way less sucky than a cheap in-your-face retcon.