The page on NOVAS clearly says that it is a computer model. Are you disputing this?
The NOVAS computer model is mainly for star predictions. Since the stars are static, I don't really consider it much a feat to model where they are in the sky. A plastic sliding star chart can do that...
Not true. NOVAS is an Astrometric package (that's what the 'A' in 'NOVAS' stands for). Astrometry concerns itself with the
precise location of celestial bodies. A Planisphere ("plastic sliding star chart") can give you a general idea of where in the sky to look for a particular bright star; if you think this is a substitute for real data, I can see why you believe some other of the things you claim to believe.
The stars aren't even static at the precision NOVAS is capable of operating - down in the milliarcsecond range. NOVAS uses a star catalog as input data for star positions (several good ones are available); if you want to know the precise location of a solar-system object, it uses an ephemeris as input data, but this is optional. The JPL ephemerides are commonly used for the major solar-system bodies - the NOVAS documentation tells you what you need to know to use these - but others are available as well. Even if you're not interested in solar system objects, NOVAS still needs to know where earth is relative to the Sun and solar-system barycenter, so it has a built-in ephemeris to calculate that, at slightly lower precision than the better external ephemerides. If you're looking at the NOVAS documentation, see the section about the solarsystem v.1 and solarsystem v.3 routines; which of these and which ephemeris you use determines which the solar system bodies are available. Once NOVAS has the position of a celestial object in one of the coordinate systems it can work with, and your location (otherwise the geocenter), it will tell you where it is relative to that location (in your choice of the coordinate systems it supports); it doesn't care if it's a distant galaxy, star, or solar-system object.
But in regards to the Lunar Eclipse, that is a little more complicated to predict, since it requires orbital dynamics. On NOVAS the link for the Lunar Eclipse predictions are three levels down, and that page says that the times come from the Astronomical Almanac, and also links us to another page for "more info" where we read that eclipses are predicted for 1500 to 2100, which is not something a geometric model, which can predict anything at any year, would state. The range of eclipses sounds more like some astronomer in the past computed those date ranges using the saros cycle.
Where "on NOVAS" (information pages or documentation?) is the link that leads to the Lunar Eclipse predictions pages you refer to? Since NOVAS is not concerned with eclipses
per se, I was surprised to see there would be such a reference, and, since I haven't seen any that are obvious, without exhaustively following all paths down three levels, I can't find it. NOVAS could certainly be used for this purpose, but I doubt many are using it this way. I can think of one person who might, but I'm not sure he's using NOVAS.
The geometric model which "can predict anything at any year" that you refer to simply does not exist. If you are looking for precise predictions, solving the N-body problem for all reasonably-well characterized solar-system objects (including moons and many large and not-quite-so-large asteroids), all of which affect each other at least somewhat, with relativistic effects addressed as needed, is far from trivial. Even if you don't need overly precise predictions, far into the future or past, even very small errors accumulate to become significant. This is not even remotely a "charting" operation.
"Sounds more like". In other words, you're guessing. Do you have any evidence that this is the case? The NASA page says that Saros is used to catalog eclipses; they do not say they they use Saros to predict them, so please don't bring that up again.