Hey there @EstimateAssist; thanks for joining our Community and using Paper!
While tasks will always appear crossed out when completed you may want to use check-mark emojis for a similar visual effect instead.
I'm not sure if this would help, but you can also add your custom emojis from the emoji list; just scroll all the way down to the bottom of the list until you see the relevant option.
Alternatively, you could use tables and note any tasks as done manually.
If you'd like to see an option for task lists to appear without the strike-though when completed though, I'd recommend posting it on the Paper Ideas section so that other users can up-vote your suggestion to show their interest.