Debut album: Beam This Up
Sophomore slump: The Miracle Workers (tried for a whole gospel-influenced thing, didn’t fit with the fans)
6-albums-later comeback smash: It’s Green
Michael Jackson’s Nose
Michael Jackson’s Money
Michael Jackson’s Career
Michael Jackson’s Sanity
You forgot Michael Jackson’s Melanin.
No doubt. We could probably get a three-day festival’s worth of bands off of Michael Jackson alone.
Hey, you think he’d headline? 
Mountbatten’s Leg.
But the OP uses Gary Burghoff’s Hand, which is a deformity and not something he lost.
Gary Coleman’s Kidneys.
Terri Schiavo’s Brain
I was in an improv group in college I named
Freud’s Prosthesis
after his prosthetic jaw that’s a plot point in The Zoo Story.
Other potential names:
Rex Harrison’s Eye (or Sexy Rexy’s Eye)
Helen Keller’s Bright Blue Eyeballs (Keller had her real eyes surgically removed and replaced with blue prostheses- this was largely due to vanity as her real eyes were so obviously blind)
Cervantes’s Arm (he lost the real one at LaPanto)
Totie Fields’s Leg
Mabel King’s Legs (Mabel King was the triple-plus sized black actress bka Mama from What’s Happenin’? and was later a double amputee)
John Milton’s Vision
James Thurber’s Vision (and nasty disposition from all I’ve read)
Alexander Graham Bell’s Mama & Baby Mama’s Hearing (AGB’s mother and wife [two different women] were deaf- it was actually his experiments to find a hearing aid that led to the telephone)
Kaiser Wilhelm’s Arm (Kaiser Wm.2’s arm never grew after a serious horseback accident as a child, but in his portraits it’s fully formed and in photographs it’s shielded; he was very sensitive about it)
(Henri de Toulouse-)Lautrec’s Legs
Homer’s Eyes (or vision)
Gouverneur Morris’s Arm & Leg (Morris was one of the most colorful of the U.S. Founders; he lost his leg in one accident [drug by a carriage wheel] and the use of his arm in another.*
Washington’s Teeth
*That’s Morris with the peg leg on the mural in the National Archives, but it’s probably idealized.
He was the poorest member of one of the nation’s richest families but became possibly the richest man in the nation due to his business acumen and bought the family estate. He was a metrosexual long before it was popular but did not believe in marriage so he kept a stable of mistresses; when he decided to marry and have an heir late in life he proposed to Thomas Jefferson’s cousin Anne Cary Randolph who he did not actually know personally (they may have met) but became fascinated and began a correspondence with her while she was on-trial for murdering a newborn babe in a case that had accusations of incest and adultery. As a wedding gift he allowed her to fire all but one of his mistresses. (He’s also responsible for the Constitution as it appears today; the original was a printed version but he refused to sign it because it was ugly and wouldn’t look good in a museum.)
Well, borrowing part of a band’s name (and keeping with the Sandy Duncan theme) how about
Second Eye Blind ?
Chris Burke’s Chromosome
Ding ding ding, we have a winner. 
Hey, no dissing Corky or I’ll sic my rabid-Life-Goes-On-fan mother on you!
I believe the theme is “things they’ve lost” correct? Even jayjay stressed this in posting 19.
Anyway, many people think of Down’s Syndrome as being caused by a missing chromosome. Being “Dopers”, I’m sure we know that the condition is called trisomy 21, meaning the 21st “pair” of chromosomes actually has 3 instead of 2.
So, Chris Burke has an extra chromosome and not a missing one.
Actually, the original (unspoken) idea was not necessarily something lost, but any sort of deformity- missing hand, extra hand, small head, large head, no head, etc., for example, Marty Feldman’s eyes would work, as would the previously mentioned Milton Berles dick, etc.
Wee Bairn
Okay, I agree with your clarification. I guess I was just being nitpicking.
That is insensitive, offensive and completely uncalled for.
(WHY THE HELL CAN’T I STOP LAUGHING?)