However, the Judge could do this: hand down a sentence and either put him on probation or vacate the punishment.

The conviction stands regardless of whether and when he's sentenced.

He's not legally a convict until the judgment is entered; that happens after he's sentenced, with the sentence forming part of the record.

He hasn't been sentenced.

He's been found guilty so in lay terms he's been convicted.

Do you want to use expert usage of the word or the lay usage? (Keep in mind the choice in other areas of academic life--do we want to use medical terminology for a thing or the lay terminology?)

Personally, it's a choice I don't have to make because it's never been a topic of conversation for me, apart from meta-discourse like this one--discourse about discourse.

different realms of conversation to me. One is the strictly legal argument in that you are correct, he isn't technically convicted.
In the other context such as discussing his character, he was found guilty by a court.
So yes, he committed the crimes and it was proven, but the process is incomplete at this point.
The question that remains is can it be abandoned? I don't know the criminal system well enough to talk about that intelligently.