Would it be better for Starship to have a separate set of small fuel tanks dedicated to landing the ship, maybe controlled separately or plumbed differently.
What you are describing are the header tanks, that were present in the SN8 vehicle and should be in all Starship vehicles going forward.
A header tank is a smaller tank, that holds fuel or oxidizer. The Starship's CH4 header tanks is roughly a sphere, buried in the middle of the common dome (divider between LOX tank at the bottom, and CH4 tank on the top), looks like a pimple at the bottom.
The main fuel line runs from this header down to the engines. The main tank fills the header and when the main burn is complete, it is presumed that the header tank closes its valves on the top, and remains full until landing.
The LOX header is also roughly a sphere, in the very nose of the fairing, and holds LOX until landing time.
In this image of the current state of the Starship fleet from Dec 27, 2020 you can see the various elements in the drawings of the vehicles.
If you look at the tip of the fairing noses, you will see the LOX sphere. If you look at the bottom of the common dome you can see the 'pimple' sticking down. On the SN14 you can clear see the 'downcomer' pipe that runs from the CH4 header down to the engines. The sphere in the SN13 item is the CH4 header.
You will also notice that the Super Heavy (Booster Number 1 BN1) on the far right does not have any of these features, because it will not have header tanks.
The header is useful to enable restart engines when the vehicle is not fully vertical, and the main fuel tank would possibly not have fuel around the intake. The Super Heavy is not meant to get into that orientation during landing operations (or at least when it needs to fire its engines).
Side note: Brandon Lewis who is making these updates is doing a spectacular job! Well done indeed!
Side side note: Rafael Adamy also does these schematics which are awesome.
Brandon also made a schematic for decommissioned Starship vehicles which has a nice view of the LOX Header test tank.
You can visualize the plumbing (as theorized by fans (Rafael Adamy), not SpaceX generated) in this theoretical view.
And it looks like the plumbing in the latest Startship is about to change, which Rafael did an amazing job of visualizing.