Bill, if an aircraft meets LSA criteria, a sport pilot can fly it, regardless of whether it's a Type Certified aircraft, an E-AB, an E-LSA or an S-LSA.

§61.317 Is my sport pilot certificate issued with aircraft category and class ratings?

Your sport pilot certificate does not list aircraft category and class ratings. When you successfully pass the practical test for a sport pilot certificate, regardless of the light-sport aircraft privileges you seek, the FAA will issue you a sport pilot certificate without any category and class ratings. The FAA will provide you with a logbook endorsement for the category and class of aircraft in which you are authorized to act as pilot in command.
It's a distinction without a difference. The operating limitations of an aircraft might state that one must have a type category and class rating, but it's okay - I'm still authorized based on my Sport Pilot certificate.

I'm Single Engine Land, and have both endorsements for aircraft over and under a Vh of 87 knots.

With a few caveats - obviously, both conventional gear and operating in controlled airspace need additional endorsements.

The limitations of the aircraft might exceed the limitations of a Sport Pilot, though. For example, an aircraft might be equipped for flying at night or even IFR. Doesn't matter - a Sport Pilot can't fly in either conditions.

In the case of my little Noop, it's not referred to in any way as an LSA. It's a straight E-AB. It's a single engine land aircraft that meets every criteria of an LSA (weight, cruise speed, stall speed, etc.), so naturally I'm authorized to act as PIC.

Here's something that may make your eyebrows rise - there is no requirement that a Sport Pilot train in an LSA eligible aircraft. It need only be Single Engine Land. Since the Sport Pilot isn't acting as PIC, the door is open to perform a flight review in a Cessna 172, a Citabria, or a Cessna 152 (all of which I've done). A Sport Pilot student must perform his solo flights and initial check ride in one, of course, as he's acting as PIC.

https://www.ecfr.gov/cgi-bin/retriev...se14.2.61_1303