The center of mass should be pretty low relative to the height of the lander, the engines and propellant are the heaviest parts, the engines are obviously at the bottom. The heaviest component of the propellant is the LOX, which is also at the bottom.

This is false most of the fuel is gone by the time it lands and most of the payload is up high that's why the latest designs for starship have diagonal thrusters 2/3 of the way up the rocket so they can stabilize the top heavy part of the rocket without having to control it from a high moment arm

Starship carries ~1200t of propellant, of which ~950t is LOX, and 250t is Methane. While yes, most of that will be burned off by landing, it'll still need enough to return to lunar orbit. Even if we assume that only 10% of the fuel is needed to return to orbit, that's 95t right on the bottom with another 10t of engines and most of the 100t of dry mass of the Starship itself (plumbing, tank domes etc).

The thrusters you're (probably) thinking of are the landing thrusters that NASA thinks they might end up needing. Not to stabilize the rocket when on the ground, but because the Raptors might be too powerful and might dig out a crater underneath the vehicle when landing on an unprepared surface (such as the Moon, at least before a base is established or something is sent to prepare a proper surface). Placing weaker landing thrusters up top eliminates this issue, although at the moment they're still considered speculative in the sense that last we heard (which was admittedly a year or two ago), SpaceX are not convinced that this will be an issue.

Thrusters would anyway be a crazy approach to preventing a crewed vehicle from tipping over, as you wouldn't want them to be firing when the crew are doing any of the things that would involve the ship becoming potentially unstable (eg unloading cargo). For stability they'd have to use the large self-leveling legs from the original HLS design.