Agile is popular, but good project leaders know that there is not a “one size fits all” method. If you are going to use Agile, consider how it may need tailoring to meet project goals better.
For example: If a deadline is critical, the principle with a substantial negative impact is accepting change at any time. If you eliminate that principle, your product backlog might need to be the result of a more robust, upfront elicitation to avoid delays. You can still develop iteratively, involve the business owner, and deliver practical solutions at regular intervals.
If the process eliminates most or all principles, you may want to rethink if Agile is the best method to use for the project.