LTspice - analyze current with varying resistance
The are (at least) four fundamental methods for varying a load in LTSpice. For your application I think method 3 is going to be the winner, but let me outline them so you can evaluate:

Method 1: .step

As in your question, simple but no time domain control.

Method 2: Switch Model

Good for time-domain control of step-wise resistor changes. The presence of the switch model in the current path can complicate things, and gets cumbersome if there are lots of step-wise changes.



Method 3: Variable Parameters

Set your resistor's resistance to an expression involving V(netname), and then drive that net with a variable voltage of your choice.



Very simple to include in circuit and very powerful to control because you can use any voltage source circuit.

Method 4: Behavioural Sources

Similar to Method 3, but use a behavioural source (bi or bv) instead of a passive component.



Adds the extra feature of controlling a source rather than a sink.