Consider this dialogue (only the third utterance is made up by me; the rest is from here):
A: "You could1 send him an email."
B: "Yeah, I could2 send him an email, but I won't; he only checks his email about once a week. I'll phone him."
A: "He could3 be in a meeting right now. You want to check the schedule before you do."
In my opinion, could1 and could3 share the same usage of expressing factual possibility here, the first utterance representing a suggestion and the third an uncertain assumption. Besides, could3 could be substituted for may with the meaning more or less unchanged.
As for could2 I would think it's another story. I won't in the utterance cancels the implicature that "I" am likely to send him an email. Thus, I think could2 is different from the other two could1&3. The other reason for my thinking is that could2 couldn't be substituted for may in the context because may itself isn't in a preterite form for hypothetical thinking (but might would be an alternative for the second utterance), so I believe could2 is a purely hypothetical version of can. ( But I'm not sure whether could2 has the same usage as in  The Cambridge Grammar of the English Language, aka CGEL.)
If we try to backshift the last two utterance we can see the difference:
I could2 send him an email, but I won't. ⇒ I could2 have sent him an email, but I didn't. #1
He could3 be in a meeting right now. ⇒ He could3 have been in a meeting just now. #2
I think #1 is a remote (conditional) construction while #2 is a modal perfect construction, which demonstrates in the original dialogue could2 is different from the other two could1&3.
Is my understanding on could2 and could3 correct? And is my proof method valid?