Pumpkin Scissors/WMG

The anime is entirely a series of in-universe propaganda films put out by the military to promote its public image and vilify the moribund aristocracy.

 * The only noble family that still retains real power due to its military ties, the Marvins, paid to have their daughter star in it. Alice has only nominal officer duties and is just a very hammy actress. Section I was used as a scapegoat to distance the military as a whole from its war crimes. In a propaganda film, it's also more expedient to blame the awful economy on aristocratic greed than complex factors that are hard to understand.

The unit's name was originally Jackknife, not Pumpkin Scissors.

 * The pumpkin with shears logo was simply a visual pun, pairing a jack-o-lantern with cutting utensils, hence "jackknife". Some moron bureaucrat confused the written description of the logo with the unit's actual name. There's no way Pumpkin Scissors is a real name.

The Weapons Research Division is the Pumpkin Scissors version of the nameless company for which Dilbert works
"Miraculous burn cream? It'll never sell. Let's make a supersoldier."
 * Their eventual defeat will likely be a massive Take That against inefficient engineering everywhere.

The Invisible Nine, despite all the supersoldiers, was a massive failure

 * Seeing as The Empire didn't win and the super soldiers are now just doing whatever they want, this seems likely.

The Lanterns that 901-ATT used work by feeding off of energy from the user's soul
Maybe the energy is what normally controls human emotions. When the energy is used for something else, the subject becomes completely emotionless.
 * Or it uses a post-hypnotic suggestion, forcing the user to use the lantern as a kind of cue to go into killing mode. Plus the psychological effect they probably have.

The world of Pumpkin Scissors takes place on another continent of the same world as FMA
Not much to explain here.

To go with the above, Alice is related to the Armstrongs

 * Unthinking heroics and women with swords have been passed down through generations!!! (One boy, three big sisters, one of whom joined the military... I can't wait to see how her brother turns out.)
 * All she's missing are the sparkles...

Like FMA, Pumpkin Scissors has alternate dimensions.

 * After alot of looking, this troper concludes that the world of Pumpkin Scissors could be crossed with Avatar: The Last Airbender and Randal is actually Teo. After the Kauplan institute found out about the crossing of universes, they somehow found Teo after the defeat of Ozai but before the war in the Pumpkin Scissors universe. They saw the boy and his spirit and thought he would make a good soldier. They take him, erase his memory, experiment on him, manage to get him to walk, get him the lantern, do this that and another thing and BANG! Teo has now become Randal Oland. Only, instead of being the Airbender spirited Teo that everyone knows and loves, he is now... well, Randal.

The distribution of advanced technology is like in Fringe.

 * Random distribution of advanced technologies and experiments run rampant over the Empire? Mysterious benefactors just giving out tech that could have won the war for either side? Someone's experimenting, only with the whole Empire as their lab.