So to be clear, “continuous” means you can’t break the paperwork seal. Once you do, you can’t go back to original no matter what you do. Not even with a conformity inspection?
Remember that there is no change in paperwork. A standard category aircraft that meets the LSA definition will not say "light-sport" anywhere on it or in its paperwork. It simply meets the LSA definition by virtue of its specifications and performance. But your basic principal is correct. If an aircraft that meets the LSA definition is somehow modified so as to fall outside the definition, it is no longer eligible for operation by sport pilots. Nothing changed in the paperwork, but the airplane physically does not meet the LSA definition any longer. At that point, even if the aircraft is then changed back to its original configuration, it is still ineligible for operation by sport pilots and will always be, because it has not
continually met the definition of a light-sport aircraft.
It must also be true that an airplane that starts out at a slightly higher gross weight than 1320 pounds can not be modified to a light sport even if the modification is allowed by the TCDS?
Correct. The aircraft you describe has not met the LSA definition continually since its original certification. It was initially ineligible for operation by sport pilots, so it will always be ineligible no matter what happens down the line.
My Champ started out its life with a gross weight of 1350# and was modified to a gross weight of 1300# by changing its landing gear to standard oleo struts. Complete with 337 documentation and logbook entries. It has been flown in the light sport category for years. With the Part 1.1 definition, this isn’t legal and my Champ is not, and never will be, a light sport aircraft. I may as well go back to 1350# and be done with it?
Correct. Your Champ has NEVER been eligible for operation by sport pilots, and if it has been operated as such these operations have not been legal. You might as well put it back to 1350 and enjoy the extra useful load.
As an aside, you can thank the folks at the Cessna 120/140 for this restriction. Back when the light-sport rules were still in discussion and being issued as a notice of proposed rulemaking (NPRM), the 120/140 club jumped the gun and applied for an STC to lower the gross weight of their airplanes so as to make them eligible. The FAA basically said "Oh sh*t, if these people thought of this, a lot of other people will try it too. That's gonna be a mess". So they specifically wrote the rule to prohibit this from happening. Yes, you can lower the gross weight, but it won't make the aircraft sport pilot-eligible. Boom.
If the 120/140 club would have waited until after the final rule was published, the FAA might have missed that loophole. But we'll never know.