Maybe even have a backup evaluater ready to go in case the third one backs out for any reason.
I would definitely second that recommendation.
I had a problem with one of my evaluators. She wasn't answering my emails, and I had a feeling the phone messages I left at work weren't getting to her...as much as I stressed the importance to the receptionists.
🙄 Finally, something like 3 days before the deadline, I talked to a receptionist at work (we had a revolving door of staff members, so they didn't know I'd worked there), and asked for her. I got the usual "She's with a client, can I take a message?" I got frustrated and said "Are you sure she's not available to come to the phone right now?" To which she replied, "Um, I would have to check."

Yeah, so she went to check, and imagine that! she was available to talk, once she heard who was on the phone. I asked her if she had received the email from VMCAS, and she couldn't find it, even though I'd submitted her as an elor a while ago. So I deleted her off my vmcas and resubmitted it so she'd get the email, and had her input all of the information while I was on the phone with her to make sure she'd do it.
It was quite frustrating, and I couldn't submit my application until the day before the deadline, so I suggest you keep pestering your rec letter people until everything's submitted. They should understand how stressful the application process is, and you can figure out a way of pressing them without being annoying, like asking when you can expect their rec letter to be submitted, or that you just wanted to double check to be sure they were aware of the deadline.