By happy accident, I stumbled across this story while looking for something else. It's "Marooned on Planet Earth" (1985) by <PERSON>. The only publication listed in ISFDB is the March 1985 issue of <PERSON> Science Fiction Magazine, which must be where I had read it originally.
My memory was fairly distorted, so I'm not surprised that nobody recognized it. The fact that the protagonist is a normal person seeking the transformation voluntarily is established in the first lines:
"Why do you want to be an alien?"
<PERSON> smiled at the question. Wasn't it obvious?
The doctor leaned forward, perhaps to get a better look at <PERSON>'s smile.
<PERSON> cleared his throat, and the doctor's head made a small anticipatory nod. But <PERSON> remained silent.
After a moment, the doctor said, "I understand. You feel helpless, out of control, yes? Adrift in a lifeboat, perhaps. Rudderless. Becalmed under a broiling sun, yes? You feel your life slipping away, dribbling out, escaping into thin air. You want a purpose for living. You want life to be an adventure. Yes? Is that it?"
<PERSON>'s head had started to nod almost from the first and was by now rocking up and down emphatically. "Yes!"
The treatment involves begin given the illusion that the patient is an alien on a mission:
..."Sign both copies. In four months you'll return for an evaluation. Don't worry about remembering, it's all built in." He quickly unfolded <PERSON>'s hundreds and gave the bills a snap, peering at them briefly in the window's light. "Very good." He glanced at the signed forms, pulled a carbon for <PERSON>, and shoved the rest into a drawer. "Relax!" he said. 489
"The next thing you know, you'll be waking up in bed tomorrow morning. And when you do--"
"I'll be an alien."
"Guaranteed."
"With a secret mission."
"Absolutely."
The process is some sort of hypnosis:
The alienist's arm shot into the air and wiggled like a drunken snake. Then his fist opened and <PERSON> was staring into a battery-powered Hypno-lite®. Brilliance swelled to a fascinating conclusion.
And that was the end of <PERSON>.
Shortly after waking up, the "alien" Xgglm sets about improving the situation of his host:
Next he examined his unprepossessing host. Another mess.
Later, when he had consulted information storage devices in the nearby emporium called a "library," <PERSON> confirmed that his adopted body was sheathed in excess poundage of subcutaneous gelatinous fatty cells. Fortunately, there was plenty of easily understood advice concerning the removal of this unhealthy mass, and <PERSON> set about the task with enthusiasm.
He also learned that the brain of the beast--which he was forced to use--contained a vast and easily manipulated data storage and retrieval system, virtually empty at present. He commenced filling it with the contents of the library, for it was impossible to know this early in the game what information might lead to his escape.
<PERSON> concluded he might require an added measure of strength, so he put himself on a program of exercise and muscle building. As the body neared the maximum of its potential, <PERSON> took it outside to cooks its skin in the ultra-violet--a "tan" being highly prized by the natives.
His mission is apparently nothing more than the need to get off the planet, which will require a ship that can't be manufactured with current technology. To that end, he seeks out a local UFO enthusiast club, where he meets someone that he knew from high school:
The group called itself the Extraterrestrial Propulsion Society, and was concerned with the location of alien spacecraft. There was no doubt--judging from the incredible accounts--that these flying saucers (as they were frequently called) were precisely what Xgglm sought.
Within minutes he was on the Hollywood Freeway in his new Corvette. He got off at Roscoe, and was soon traveling east into the hill of Tujunga.
It was noon and the sun was hot, the air spicy with sage from the chaparral. He pulled up in front of the house listed in the newspaper.
...
"Who?" said <PERSON>, rapidly searching his memory files. <PERSON>... <PERSON>...
"<PERSON>," she said. "We were in high school together. But then you were... <PERSON>, you look great now."
<PERSON> grinned the grin he learned from <PERSON>. 652