Although there are many people that claim that "none" and "neither" should always take the singular form, it's always sounded odd to me, so I decided to dig into it a bit further.
For example, here is an Ngram of "none of us is" / "none of us are":
In this case, we can clearly see that "none of us are" - i.e. the supposedly "ungrammatical" form of the sentence was vastly more popular until roughly 1880. In 1880 or so "none of us is" began to take hold, and in the 1920s there was a steep decline in the use of "none of us are" - perhaps in response to overzealous copy editors enforcing the so called rule.
Most interesting is what's happened since the 1990s, where "none of us are" has shot back to prominence, leading to the fact that "none of us are" is now the dominant form again.
As suggested by snailplane, here's some interesting additional reading which seems to confirm my opinion that "none/neither should take the singular" is a wholly invented rule:
As a native speaker, I've always just gone with choosing the verb as if "none" or "neither" was not taking part in the verb choice.
The sentences are too long. -> None of the sentences are too long
A or B is the correct answer -> Neither A nor B is the correct answer.
The guiding principle should be don't use Past Perfect unless you really have to.
The uncertainty occurred after the asking - chronologically, and in the narrative sequence of OP's text. That's what normally happens when you report a series of events...
I did this. Then I did that.
It's grammatically possible, but completely pointless in most contexts, to express that as...
I had done this. Then I did that.
In OP's second example, it's pretty much impossible to avoid Present Perfect with the word must. You could get away with ...but it must be [that] you forgot..., but it's a bit "starchy". Present Perfect is perfectly natural here.
Consider, for example,...
1: You didn't answer the doorbell when I rang, so you must have gone to work early.
2: You didn't answer the doorbell when I rang, so you must have been in the shower.
Clearly in #1, the action in the present perfect clause (you going to work) happened before the simple past (I rang). But in #2, you being in the shower happened at the same time as I rang. That's not a problem in English; if the chronological relationship between actions is obvious from context, it doesn't always have to be made explicit by the verb forms.
Best Answer
They are both correct but emphasize different aspects of the accustomization.
The first emphasizes the final state: you will be accustomed to it soon. I.e. at some point in the future (soon), you will find that you are used to it.
The second emphasizes the transition: you will become accustomed to it soon. I.e., you will soon undergo the transformation from "not being used to it", to "being used to it."