How was your experience asking a PE teacher or coach to do the CFA test for you? I don't know who and how to ask.

i asked my coach and just did the CFA it wasn’t that big of a deal lol, just tell them you have to take a physical test for the naval academy and explain to them what it is and they’ll be happy to help
Any of your HS gym teachers or coach will likely be more than happy to help you with it. Have the form with you to give to them so they can prepare. Our DD asked her hockey coach and she said she would be honored to administer it for her. Practice the basketball throw a lot; repetition is the key to this odd test. Plenty of good videos online demonstrating technique.
Kid used his X-Country/Track coach first year. He was happy to do it.

Second year, he used his LT advisor from his NROTC unit (an Academy grad).
My XC coach was happy to help. Just make sure you let them know what the test entails. There’s a pdf with instructions for the administrator so just print and bring that and make sure you are ready.
For anyone applying to more than one Academy, ie WP, be sure to video the required events per instructions. This will save you from having to redo it.
Also be sure the person doing the evaluation understands the CFA instructions.
Sit down with the proctor a day or a week before the CFA. Review the instructions together, carefully and in detail. Walk through the sequence and procedure and locations. Be clear about what they do and what you do.

As noted above, PE teachers are usually happy to proctor the CFA. But don't assume that they'll know exactly what to do. Minimize the surprises and glitches by doing this bit of prework. You won't regret it.
I was rejected to SLE and NASS
So you also applied for West Point. Not sure if it is same for any region but we live in DC area (Southeast Region) with very supportive FFR on helping CFA. DS did ask his PE also a X-Country coach to administer his CFA once. He did not do well but later he was reached out by West Point FFR from an army base in VA and they offered CFA training/recording from the summer to the winter next year (before the application deadline). DS would not have passed his West Point CFA without their help. They also did his Naval ROTC fitness assessment. They will do all SAs CFA and ROTC (army, naval, naval-m and air force) fitness and they will help you to improve.
They will be happy to do it for you, just know the CFA instructions that come from the portals and websites beforehand in case they've never done it before, chances are they have though. Also, definitely try to do it as early as you can and don't wait until the last minute!
Is USNA still only SA that accepts coach proctoring? Much easier for coach to do it as DD hasn't had PE since 1st semester freshman year but not a huge problem if USAFA, USMA, etc won't accept coach doing it. Ideally she wants to only take it once for all SAs.
USAFA accepted my kid's when he did it for USNA and USAFA together. I think USMA will as well, but they want it videoed if I'm not mistaken.