Firstly, I am sorry you had a runaround - very boring.
Secondly, your interpretation of last/this/next [day of the week] is what I would expect, so stick with it and don't allow this sort of experience to confuse you.
However, on reflection I will qualify that to say that if on a Monday you want to refer to the Wednesday in the same week, I would say simply "on Wednesday".
To make it absolutely clear for an appointment I would also include the date.
As to move it up/push it down - if referring to moving an appointment to a later date, I would say "Could we move that up to xxxx?"; if it is to change to an earlier date, I would say "Could we move that back to xxxx?". I haven't met the use "push it down".
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