I can't find the thread where this was discussed, but I did say I would provide an update. As of 6/27/16 if you're on the More Everything plan you can still get the month2month discount once you are no longer in contract. You however can no longer apply the discount yourself via your web account, you have to call or chat.
I won't know until my next bill that it actually went through without issue.
Because of your post, I just tried calling in to add this discount to my line which recently completed its contract. The CS rep wasn't sure if it was still available to be added so he checked his system and said he WAS able to add it to the line in question. I don't expect another bill for 18 more days so I won't know for sure if it has been added until that time, however I went into my MyVerizon account to see if the discount was attached to the line by trying to upgrade a different line. When I did so and my expected bill was laid out, the line which had just come out of contract DID in fact show up as having the month to month discount.
Like rcschnoor, I can SEE the discount on my account (along with the other month2month discount that was applied a year ago) so I imagine I won't have any issue. It's already adjusted my bill total under my account.