Submit the secondaries so they are complete except for the letters. That will help 🙂 Always better to have everything done that you can get done.
As for letter writers taking forever...
I asked all my letter writers back in March, just to make sure I had everything in order. I kept contact with them every few weeks, just to remind them I was alive and such (I knew them all fairly well).
When AMCAS opened I sent them the LOR letters the first day.
Professional Letter writer: Sent 1st day, in AMCAS in less than a week.
Science Letter writer 1: Sent 2nd week, in AMCAS before June.
Science Letter writer 2: Had not sent letter by mid-June. No longer responded to emails/calls. I ended up finding her schedule for the semester and basically waiting outside the building where she taught (as she was not present for office hours for 2 weeks). Turns out, her daughter had been in the hospital for the past month and a half and she felt horrible about not responding/sending the letter. After talking about her daughter for about 10 minutes and her venting I offered to have someone else write the letter to give her extra family time, but she insisted on writing it for me and sent it in the next day. **** happens to professors sometimes.
Non-Science Letter writer: I knew this professor the best, as I wrote my honors thesis under her guidance. I had been in contact with her for over 4 months about this letter, letting her know it would be early May before the letter could be submitted. On May 6th I get an email stating she's out of the country until late August with no access to letterhead or a printer until then. So I had to find someone else who still hasn't sent it.
Peer Letters: Both sent by mid-June.
Moral of the story: 1) All letter writers are different and it really just depends on outside circumstances sometimes.
2) I cannot write a short post.
3) I also learned 90+% of professors don't like to upload LORs. I have no idea why. It seems so much faster and easier, but every person I asked mailed it, which of course took longer to input.