The help centre has the following to say on accepting answers:
What should I do when someone answers my question?
Decide if the answer is helpful, and then...
Vote on it (if you have earned the appropriate voting privilege). Vote up answers that are helpful and well-researched, and vote down answers that are not. Other users will also vote on answers to your question.
Accept it. As the asker, you have a special privilege: you may accept the answer that you believe is the best solution to your problem.
Accepting an answer is not mandatory; do not feel compelled to accept the first answer you receive. Wait until you receive an answer that answers your question well.
Help Center > Asking, Someone Answers
What does it mean when an answer is "accepted"?
When a user receives a good answer to their question, that user has the option to "accept" an answer. Acceptance is indicated by a colored checkmark next to the answer that has been accepted by the original author of the question.
Accepting an answer is not meant to be a definitive and final statement indicating that the question has now been answered perfectly. It simply means that the author received an answer that worked for them personally. Not every user comes back to accept an answer, and of those who do, they might not change the accepted answer even if a newer, better answer comes along later.
Help Center > Answering, Accepted Answer
From this we can see that the official standpoint is for accepted answers to be:
- Helpful to the OP
- The best solution/most helpful to the OP
- Works for the OP
These are general guidelines, however, and it is generally solely up to the OP to accept whatever answer helps them the most. Even looking at bullets 1 and 2 we can infer that it is generally fine to accept an answer that is helpful to you.
Why shouldn't you do this?
It's not guaranteed to work. Whilst the answer could gain a few upvotes it could also gain some downvotes increasing the gap. Also if the question is about ready to fall off of the HNQ the gap is likely never going to be made up. Even on a fresher HNQ one but with a big starting gap it is unlikely to work.
The acceptance/reputation switches can annoy the other users.1 When my answer gets accepted I feel quite proud that my answer helped the OP the most enough for them to change their acceptance. This is particularly the case when I answer an older question with an already accepted answer (for a recent case of mine see here). It isn't the best to have that changed back to the original accepted answer again.
Then the "main" accepted answer user could get a bit frustrated to see the +15, -15 and +15 again on the same question. If it helped you the most why would you keep changing it from them? If another answer comes along later that you want to feature would you then take it away and reinstate again and again? This could be quite annoying.
What could you do instead?
Use a bounty, it is perfect for your use case here. In fact one of the bounty reasons even fits what you are trying to do.
Reward existing answer
One or more of the existing answers is exemplary and worthy of an additional bounty.
In the custom bounty message you can then state the answer you are bountying with a link to it and more importantly a reason why.
A bounty also has the added side effect that the question will stay featured for a week and so the answer is guaranteed at least a week in the spotlight whereas acceptance can't really guarantee any spotlight outside the question itself.
1. On a note here that this point will be quite subjective and vary from user to user so YMMV. Also note that I'm talking about people taking votes personally, whilst this shouldn't be the case in general people take them this was because it is human nature after all.