For anyone that experiences a problem with Depth Perception at MEPS, hopefully here is a story to persuade you that you are not screwed. I was an SNA applicant going through the Phoenix MEPS command in Arizona. After initial briefing, we were taken into a room to check vision. I was determined to have 20/20 and passed everything until it came to depth perception. I was asked to perform the Randot test with the special glasses on, the nurse applying the eye exam asked me to hold the randot page at arms length (which for me is around 36 inches) in which I couldn't determine the odd dot out for over half of the numbers required. This problem wasn't prevalent until I got all of my waivers, but was DQ'd because I didn't pass depth perception.
I followed up with what my Recruiter said had to be a Military Optometrist by driving from Phoenix (mid Corona Virus) to Vegas in order to meet with a retired Air Force Lt Col that was an optometrist at Nellis. He proceeded to cuss out the woman from MEPS because the test is supposed to be administered from 16 inches, or regular reading distance. After the re-administering of the test I was able to get a waiver and cleared for active duty as a Naval Aviator. He proceeded to tell me that students passing this test on those standards were actually far sighted and can't properly perceive depth in a tight environment (aircraft cockpits).
So don't be afraid to challenge a decision by MEPS with a specialist if you really care about getting in.