Thinking more about this, I feel a good solution might be to let students decide whether they want to keep the first semester letter grades once they receive them, or simplify them down to a pass/no-pass.

That way there's still an incentive to do good work, and students who do well still get to receive the benefit of keeping the letter grade. Students who do poorly receive the letter grade as feedback, but have a one-off chance to reduce the impact and try again the next semester.