How can I use lerp to rotate an object multiple times?

My situation is this:

I have an object whose rotation in Euler angles is (0, 12, 0) and I want to rotate it using a lerp function to eg (3600, 12, 0). That is to say, I want it to rotate around the x axis 10 times.

I want to use lerp because I want to use an animation curve to control the rate of the spin - starting slowly, speeding up, finishing slowly. I can't use a sin curve or similar ease function as I need something more idiosyncratic, hence an animation curve I can edit. Also the end rotation and duration of the spin are set in code as they vary, so I can't use an animation. And to make it super complicated, the start rotation also varies!

My first thought was a simple Vector3.lerp between the euler angles, but this doesn't work - as Unity uses Quaternions internally it comes out wonky at the end.

I then thought I would convert the start and end positions into Quaternion values and slerp between them, but that only rotates once because that's all that Quaternions can represent.

So now I have this monstrosity:

 while (timer < spinTime)
 {
     transform.localRotation = Quaternion.Euler(Vector3.Lerp(startRot, endRot, spinCurve.Evaluate(timer / spinTime)));
   
     yield return null;
   
     timer += Time.deltaTime;
 }

Which also doesn't work because even though the start rotation and end rotation as Euler angles have the same y and z values, when converted to Quaternions they don't, so it spins around multiple axes.

I also tried manually forming the start rotation value to force the z value to remain as 0:

 Vector3 startRot= Quaternion.Euler(transform.localEulerAngles.x, transform.localEulerAngles.y, 0).eulerAngles;
  

But you guessed it, even though transform.localEulerAngles.z == 0, the startRot this generates does not match this:

 Vector3 startRot= Transform.localEulerAngles;
  

So when the lerp starts it jumps to a different starting position.

Help!