Learn English – Usage of “I would prefer”

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.

You can use gerunds if you're using would in a conditional statement, e.g.

I would prefer walking over driving if my legs were in better shape.

But if you're just making a general statement about your preferences, would prefer is normally followed by a verb.