So, for some reason I can't even fathom, Hellsing wasn't even allowed into the psychic chamber (the name of which I can't remember). Only Combo could do it, despite Hellsing having a higher will even without psi armor. Sorry, people who voted the other way
This also led to my first attempt at save-scumming, hoping that if I gave Hellsing psi armor and switched back before going on the mission, then he'd be able to do the job. Sadly, the game had already saved after Combo touched the ethereal device. Damn you Firaxis for making save-scumming difficult!
Anyway, the final mission went well, more or less. I took way more damage than I should have due to little things like not realizing that psi or archangel armor ARE NOT immune to poison or fire like the titan armor is, or not realizing that cyberdisks can chuck grenades. As a result, everyone was at least a little bit battered and bloody by the time we reached the Ethereal Chamber, and Medi-san only had one more medikit use left.
The berserkers in the final chamber were no threat at all. A quick psi storm from Combo left them weak enough to kill with a single shot each. Those ethereals, on the other hand...
They mind-controlled half the squad in a single turn, including the supposed savior of the human race, Combo. Hellsing, Medi-san, and Socks worked together to kill the one controlling Honor, who activated her archangel suit to join Medi-san in raining death from above.
And then Combo, still being possessed, gunned Honor down. She was critically wounded, but I didn't have time to stabilize her. Hellsing fired two shots at the head ethereal, and Socks ran in to deliver two point-blank shotgun rounds, which finished it off. The other ethereal died simultaneously.
As for what happened next, I'll not spoil it here
After the events of the final battle, XCOM would enjoy a few more years of active service before being drastically downsized. All personnel were given a choice to either stay with the agency or return to civilian life (after signing a stack of legal documents thicker than carapace armor, of course).
Hellsing went back to his home in England, where he received a knighthood from the Queen herself in honor of his achievements. After a couple decades of private life, he joined XCOM again, but in an advisory capacity. He still practices with his rifle, but he'd be the first to admit that he lost his edge long ago.
Socks requested a plane ticket Scotland, where he disappeared. His current location and status remain unknown to this day.
Honor never quite adjusted properly after her experiences. Being mind-controlled and near-fatally shot (yet again) by one of her comrades was devastating to her psyche, and it took two years of intensive physical and mental therapy to recover enough to be released. She refused to return to Germany and immigrated to the United States instead, where she lived comfortably on a generous pension XCOM set aside for her and the other veterans.
Medi-san went home to Japan, where he completed medical school and became a paramedic. He later married and had three children: Sika, Thomas, and Martha. The three are always pestering their father for stories about the Alien War, which he adamantly refuses to discuss.
Prototype stayed on with XCOM as a security guard. He was later killed in action when a terrorist group attempted to steal the stockpiled weapons and armor though his tenacious efforts ensured that they did not get anything.
Combo was never seen again after the Skyranger flew away from the alien mothership. Although officially labeled K.I.A., some people think that, being the most powerful psyker in known history, she
could have survived. The exact truth is probably lost forever.