Learn English – How long is “a few years ago now.”

It’s a British expression, now used quite generally of university study, that used to be especially common at Oxford and Cambridge. I suspect that it reflects the way in which education was traditionally organized at those universities: a series of set-piece lectures, not necessarily compulsory, and a great deal of independent reading that was regularly discussed with a tutor, either individually or in small seminars. However important the lectures were (or in some cases perhaps weren’t), the bulk of a serious student’s time and energy went into reading, digesting what was read, and writing based on that reading, especially in subjects like history, literature, and philosophy. In this setting reading history (say) would be a natural pars pro toto.

I use just very often in speech and casual writing. I tend to edit it out of more formal writing. I am a native American English speaker from Tampa and Boston.

To me, it can have both meanings, and I don't think that I have a preference. Your examples are all ambiguous to me. I think that the meaning is often clear from context (don't underestimate the power of context!), as in:

1) I'll be there soon. I just woke up. (recently)

2) I didn't call her. I just sent her an email. (merely)

3) I tried, but I just don't understand. (simply)

I don't see how changing tenses or aspects can help you, except that the future and simple present (always?) rule out the recently interpretation. But all of the following are equally ambiguous to me (sans disambiguating context).

4) I [just ate/am just eating/was just eating/have just eaten/etc.] an apple.

When I want to be crystal clear, I just replace just with merely, only, simply, or suchlike. I think that I less often change just to recently. I think I more often say just now to indicate that I mean recently.