jIH:

Couldn't we use the prefix trick with {-'egh} and {-chuq} ?

SuStel:

Aside from breaking the rule about using only no-object prefixes with the reflexive suffixes

I'm sorry for the silly-stupid-ridiculous question that I'm about to
ask.. But I can't understand how the rule about using only no-object
prefixes with reflexive suffixes is broken.

Suppose we write:

taj jInob'eghpu'
I gave myself a knife

or

taj manobchuqpu'
we gave each other a knife

How do the above examples break the rule in question ? Both the {jI-}
and the {ma-} are no-object prefixes. Obviously there's something very
basic which I don't understand, and this worries me.

Oh, no, those simply don't follow the prefix trick rule, which is this: "When the indirect object ... is first or second person, the pronominal prefix which normally indicates first or second person object may be used."

Whether or not you think the subject of a reflexive verb can be its indirect object, you haven't used prefixes which normally indicate first- or second-person object.

-- 
SuStel
http://trimboli.name