Let's go back to the fundamentals.
VD works the same at any voltage, and for these small cables and small currents we can ignore whether it's AC or DC. So your original numbers were correct, use the current of the 24V circuit and the tabulated VD per amp per metre, and you will get the VD of the 24V circuit. The crucial take-away here is that while the VD per amp is the same as on a 240V circuit, each volt is ten times more precious. A 4.8V drop on a 24V circuit is a whopping 20% lost, compared with only 2% on a 240V circuit.
How much can you afford to lose? To answer this we have to understand a bit about LEDs and the circuit inside the tape. First of all, note that constant-current LEDs and constant-voltage ones require a completely different approach. All normal tape is constant-voltage so that's what I'll describe.
LED chips themselves are diodes; they have an exponential relationship between current and voltage, i.e. they do not obey Ohm's law like a resistor. As the applied voltage is increased, nothing much happens at first, then the current starts shooting up to an unworkable level with only a tiny additional increase in voltage. The importance of this is that is difficult or impossible to simply apply a voltage and expect to get a certain current or power, as you could with a tungsten lamp, heater or typical AC mains appliance. You have to control the current through the LED chips, and let the voltage developed across them be what it wants to be. For most white LEDs the voltage is around 3V at any reasonable current.
This is of course constant-current driving. The driver sends a known current through the LEDs and the voltage developed across them is stable and predictable and therefore so is the power. But constant-current driving is a nuisance, because all the loads have to be in series and matched for current (although they can have different voltages). Constant-voltage is much more practical because loads can simply be connected in parallel.
So we compromise. We use a constant-voltage supply e.g. 24V, a series string of LEDs making up something less than this voltage (e.g. six 3V LEDs making 18V) and then lose the difference of 6V in a current-limiting resistor that behaves like an approximate current source. Every six LEDs along a 24V tape are therefore wired in series with a resistor or two, and all such strings are connected in parallel by the bus wires along the tape. Minute variations in LED forward voltage are now swamped by the voltage across the resistors, so all the strings pass almost exactly the same current at a given supply voltage. We sacrifice the 25% power wastage in the resistors (6V of the 24V is dropped rather than used in LEDs to produce light) for the convenience of constant-voltage operation.
But now we start to see the impact of supply voltage variations on the LED current. The current-limiting resistors obey ohms law and drop about 1/4 of the supply voltage. Therefore as the supply voltage varies around the nominal 24V, the current will vary by four times the percentage. A 1% variation in voltage will cause approximately a 4% variation in current, for approximately a 5% variation in power. A 25% reduction in voltage (to 18V, about the forward voltage of the six LEDs) leaves nothing across the resistor so the current and power fall to near zero. (24V tape will not light at all at 15V)
So to operate the tape within spec, voltage drop is quite critical and should be kept to a few percent. However, light output does not decrease in proportion to the voltage drop, so it is not quite as critical as the numbers might suggest.
Tl, DR: 2.5mm cable will be fine!
