I'm not sure of a good way to re-target someone in that situation. I have let a candidate just go down that line before because they were making swift progress on it, and I gave them pretty good marks at the end for an incomplete solution that I was pretty sure they could have worked out eventually, but for other people it's much harder. I totally sympathize with the disruption of an interviewer essentially telling you "not like that" when you're frantically trying to come up with a quick and workable solution, but at the same time, you're probably not going to make yourself look good if you're putting together an increasingly obviously unviable solution by bolting on more and more logic as you find holes.
Is it:
Demonstrate to me you meet our hiring skill level by working on the problem.
or:
Find the best solution to this problem, get $200k/year
I don't just reject people who give a sub-optimal solution, but going down those unfruitful paths of solving the problem often leads to situations where they stymied and just staring at the problem trying to work out how to work around what have become larger and larger issues with that approach. At that point, I'd either want them to recognize the issue and try another approach, or ask me for advice, or accept my nudge to find another path.
It's a problem I like to give because it's a problem that's easy to demonstrate your baseline skill at and get out a simple working solution, and then we can spend the rest of the time improving and optimizing.