When I come across these answers I mark them as This is a different question posted as an answer.
To me that's the best option of the current set - it is not a review - and would make a decent question if introduced right.
The real question here is whether there should be a dedicated alternative for this scenario. I agree that it is relatively common (I'd guess 1-in-5 reviews I do in the queue are like this).
For me I am content with the this is a different question posted as an answer option - it encourages the person to think about reformulating it, and adding more questions to the site, inviting additional answers too. What's missing is the wording to encourage the user to alternatively reword the post to make it a review rather than an alternate solution.
So, my suggestion is to add wording to the this is a different question posted as an answer option to make it clear that editing it to be a review instead of a code-dump is an alternative to posting it as a new question. Something like:
Answers on Code Review should provide insights on how the question's code could be improved. Alternative solutions should include descriptions of why the alternative is an improvement. Alternatively, if you have a new question, please ask it by clicking the "Ask Question" button. Include a link to this question if it helps provide context.
For what it's worth, the other somewhat related option 'This is an "I'm having this problem too" comment' is something that should be removed ;-(