Has anyone found a way around the nerves before an APFT test, or does it last forever?

Forever.
It has nothing to do with worrying about pass/fail. It's about doing your best.
If you played any sport in high school and/or college, it happened there too before every game.
I got the nerves before every APFT where I was going to get over 290 as a young man, and I still get it now when I know I don't have to worry about pass/fail for the old man scale.
Also happened before every high school football game, college football game, college rugby match, and every rugby match during my first ten years in the Army.

The best way around the nerves is to prepare and be confident you will do well. If you are a SPC (P) or a SGT (P), then of course you want to max to get as many promotion points as possible. Otherwise, just take the test and do your best. Use the nervous feeling as motivation to better prepare for the next APFT. I try to take two approaches to things that will potentially worry me by asking a simply question; can I do anything about it? Yes) then just do what I can and not worry. No) then it is out of my hands and worrying is only suffering twice.

This is natural - and will likely continue throughout your career. I utilize the MRT skills of Real-Time Resiliency and Energy Management- it truly works for me.

I think so long as you care about your APFT score, you'll always be nervous right before taking the APFT.