Is it possible to say ' your choice *for* something' when you mean 'your choice *of* something'?
Solution 1:
OP is mixing up two different constructions...
My choice of [one out of several possible options].
e.g - My choice of chicken for dinner was made on health grounds.My choice for [some particular role which your choice fulfils].
e.g. - My choice for dinner was chicken, because it's healthier than red meat.
I can't say exactly why OP's 'choice [of] chicken as dinner' is wrong. In that exact construction, "as" doesn't sound at all good to me. But if, say, an American was talking about how he'd voted, "My choice of Romney as president turned out to be a minority opinion" sounds reasonable. Perhaps that's just because I conflate it with "My vote for Romney as president...".
Solution 2:
You are correct, these two phrases mean different things.
Compare these:
My choice of chicken for dinner [was a good one].
My choice for dinner was chicken.
My choice of (one of two or more things) ie, chicken as opposed to anything else on the menu.
My choice for (a separate object not connected to the things avaible for your choice)
The separate object could be a reason (I chose this car for the simple fact that it's the best there is) or an object/person (I chose this car for you because it's the best there is).
I think this is best shown by the fact that My choice for is not a phrase that is often heard, it sounds more like an announcement. It is best reworded as I chose ... for.