Learn English – Which would you use: full-size, full-sized, full size or full sized

It's grammatical, but it's probably not what the journalist intended. Would you like to have been president... asks whether election in the past would please you as you are now; would you have liked to be... asks whether a 'you' in the 19th century would have wanted to be president; would you have liked to have been... is asking whether an election in 1862 would have pleased you as you were sometime between 1863 and last year.

The concept you are asking about is probably not quite expressible in English by a single adjective, but "I've lost my appetite" is a phrase you can use to imply that you are not eating any more not because you are full, but rather because you cannot make yourself eat any more.

My other suggestion was applicable when relating the event later (to emotionally uninvolved parties): "I was really hungry, but after the first bite I was already thoroughly disgusted." However, somewhat more naturally, you'd describe the food rather than yourself, as "disgustingly greasy" or similar.

Note that "greasy" by itself is not necessarily negative by itself: there are some dishes that are delicious only when they are greasy.