Combining absolute and curve grading?
You have assumed that students' performance follows a normal distribution, with a grade of C in the middle of that bell curve and very few grades of A or F at the tails.  My own experience, and that of my peers, is that a typical college class has a cohort of good students who will mainly earn grades of A or B, some number of poor students who will earn unsatisfactory grades, and a few "in the middle" students.  That gives a bimodal distribution, with the valley just about where the peak is in that bell curve.

I urge you to look at past classes and check the grade distributions when you have used absolute grading.  If you don't already have something very like a normal distribution, forcing one will distort the assessment results badly.

Your question says your goal is to help students, and the problem is that assessments may be too difficult or the course didn't go as planned.

I'd like to suggest a different approach that's a little more work than artificially distorting the grade distribution, but is much easier to explain to students.  (Um, and to department chairs, if it comes to that.)  You haven't mentioned your field, nor whether your students are undergraduates, but if your examinations can have a reasonable number of questions, measure the performance on every question and then exclude from the computed grade any where performance of the class as a whole is below some cutoff you establish heuristically.  Almost everyone's grade will go up, and you can easily explain that you excluded those questions or problems that were "too hard."  (In the rare case where a student gets only the "hard" problems right, you can make an independent adjustment; that never happened to me.)  I do this with a spreadsheet that has student names in the left column, then one column for each question.

Once you've evaluated an assessment, you must look at the questions you excluded as "too hard" and If the difficulty was with the question, fix it.  If you believe the question is reasonable, then you need to review the material with the class again.  When that happened to me, I'd warn the students that they would see that question or problem again, and so they should prepare for it.

If you do this for every assessment, you will find that your exam questions and your coverage of the material converge, and after a very few semesters, you will no longer have questions that are "too hard" and you'll be comfortable with absolute grading.