Yes. Though that can also be a kind of fun. I guess it's not worth to fight over definitions.

Do you plan to progress to full power cleans later?

I'm having a bit of difficulty with hand position - the correct position for me for the deadlift phase is slightly wider than for the hang clean phase at the moment. Not sure if it's something I can practice/train around, or if it's just the way my wrists are.

Plus my deadlift is well over double my hang clean...

I do deadlifts and power cleans. My deadlift is almost double my power clean.

I like to pick the bar up from the ground. Also putting the bar down between repetitions allows me to re-set my back.

Keep practising, your flexibility should improve. I'd use the hand position of the hang clean phase also for the deadlift phase---because the weight will be so low compared to a proper deadlift that you can afford to use suboptimal positioning for this part.