The continuous and progressive aspects are used when a sentence is meant
to express continuousness or progressiveness. *paq vISIch: *I stretch my
hand to the book.

[...]

*SIch* seems to take the thing reached for as its object,

Did I miss anything in the discussion? I understood that {SIch} does NOT
mean "reach for", it's "reach" in the sense of "my arm is long enough to
touch something, so I can reach it" and not "I try to grab something".

I wasn't translating it. If you SIch something, you reach for it and get it. I didn't say SIch means reach for; I said the thing you reach for is the object of SIch.

-- 
SuStel
http://trimboli.name