Hi Rodrigo,
Whenever trying to do fixed fee projects, Artefactual has historically underpriced our work for the level of effort involved, so I wouldn't suggest using our prices as a guideline anyway! As an independent contractor, the important thing is that you are setting a price that is worth it for you.
You might consider setting an hourly rate you are happy with, and then working out a time and materials approach with the client. Give them a general time estimate, and tell them you will stop work and check in on options at X hours to revise the estimate and decide with them how to proceed. You can then discuss options to cut features or wrap up as soon as possible if the total cost looks like it will exceed the original budget and the client doesn't want to pay more, or agree to extend the time if needed to complete the original request.
If it looks like you are coming in under the original estimate at the check-in point, you can have a similar conversation: should we wrap up as soon as possible under the original feature request, so the client is spending less and you are doing less work? Or are there additional enhancements they would like to add?
This way, your pay is not tied to a fixed price for an unknown amount of effort - instead it is more iterative and collaborative with the client, and ensures that you are paid a consistent amount for every hour of labor you spend on the project.
Good luck!