Do you have any status with EVA?
And perhaps you could mention the route/date you are trying for - perhaps someone with knowledge of loadings could then comment.
I assume you mean upgrading for Deluxe to Super Business (or Elite to PL)?
If you are Diamond, you should be OK. Else as a guide, if they are still selling Z off the website a week or so from date of flight then the chances are er.. very good... (which is about as useful as the answer you got from BR!)
It does seem to be the case that the vast majority of these requests are met with "waiting list" these days. If there's plenty of availability they might call back in a couple of days (or even hours). Else they keep you hanging on until a few days out.