That is why modern instruments have both a first and third valve slide. You use the one that causes the least damage elsewhere.
Dale is 100% right about not needing the slide for fast runs. Your comment "I'm preparing for an all-state band audition where every tiny aspect counts." shows that you don't understand what the problem is! The real tiny aspect is intonation and we can adjust for that with the lips alone. Moving the valve slides allow more RESONANCE than lipping up or down, but moving the slides quickly during 16ths will move the horn around a bit adding instability to our tone. That resonance is NOT discernable on very fast passages in the low register.
If we are playing a C or D major scale, we can leave the third slide out. The third valve is used for nothing else except the D. I would not leave the 3rd slide extended for an Eb or Ab.
So, for the audition your playing will be judged. If there are intonation issues, the adjudicators look for reasons. If you properly lip the notes in tune, they have nothing bad to hear - and no reason to look for other things.
Post what you expect to be such a low frequency challenge. Maybe there are alternate solutions.....