^I believe there are rules or laws that restrict whether or not one can claim exempt. Generally, you have to be exempt in order to claim that you are exempt.
If you are disciplined enough to manage your cash flow, what you can do is file a W-4 with a large number of allowances every January to reduce your withholding amounts to zero. Figure out what your tax liability will be each summer. Then file an amended W-4 in, say, October, and have your employer send your entire paycheck, or a very large amount of it, to the IRS. One risk to this approach to be aware of is if you lose your job in October and don't get another one quickly, you would be up a creek without a paddle. Another risk, I suppose, is not figuring your tax liability or withholding amount correctly.
In the above situation you could also file an estimated tax payment by January 15th of the following year to get you within the $1000 safe harbor limit. I did that one year to avoid the underpayment penalty and it appeared to work.
Also, there are actually three safe harbors that avoid the underpayment penalty. One is being within $1,000 of your tax owed. I don't recall what the other two are, but you could see if those would give you more leeway. Google "safe harbor rules site:irs.gov" and that will probably get you the info.
It doesn't quite get you to what you want, but it is closer.