Payload already has “I would like more” priced into it
Getting less Payload plus some kind of “Lifting ST (Payload only)” is not the way to model this.
To model most vehicles, you get an appropriate amount of either Payload or Lifting ST, depending on how the vehicle works:
Machines that can push or pull large external loads – or pick them up and carry them with arms, cranes, etc. – have Lifting ST (p. 65), not Payload. Ordinary cars and trucks have Payload, but forklifts, tugboats, and the like should buy Lifting ST to represent their abilities.
If you’re pondering how to get Lifting ST for just Payload because you want a better Basic Lift to calculate the BL/10 per level capacity of Payload, GURPS doesn’t want you to do that — you’re supposed to just buy more levels of Payload directly instead of trying to buy fewer and then getting an advantage with a limiter to make up for the missing levels.
Of course, if your vehicle can manage more external loads than its mass (i.e., ST) would indicate and it has an internal carrying compartment, then you get both as appropriate to each. Buy up the Lifting ST until it suits the vehicle you’re modelling — first, because it sets BL — then buy up enough levels of Payload to get the internal capacity you’re modelling.