That large number is due to the fact that I (like necessity) lived "horses horses horses" for many years. It is not expected that you have hours like that in everything, or really anything.
🙂 It was just lucky we enjoyed and made a hobby out of something that involved animals. Very little of those hours were vet experience, there was probably only about 5-10 hours I was in the presence of a veterinarian. Please don't let it scare you, and don't think you have to quit your job cold turkey.
Training is a form of education. Just like you have been educating employees/trainees, you will have to educate owners about their pets. Project management shows that you are organized and in my opinion that does count as a leadership role if others were working with you. Public speaking and customers service emphasizes your speaking and communication skills, and probably conflict resolution as well. Air traffic control shows keeping your calm in a situation with high stakes. The skills you attained in those positions will be incredibly valuable/transferable to vet med. Compared to a young traditional student who has tons of animal experience, but no real world experience in human interaction/workforce, you have the leg up on those skills.
Just shoot to get as much quality experience as you can; I would say absolute minimum to start with is 100 veterinary hours. Since you are applying to vet school, you need to make it clear to admissions that you know what the vet profession is all about.
You are far from the first person to make vet their second career, and admissions knows that. With how the ranking process works, if you have very strong grades you also get a little bit more flexibility with your experience to helpfully keep you in the top 20 who are admitted.