To avoid unnecessarily using the first-time homebuyer exception, instead of making a regular distribution of $6,000 you could obtain an explicit return of contribution from the traditional IRA. Any investment gains on the $6,000 returned contribution would be required to accompany the $6,000 distributed and would be subject to ordinary income tax, but you could apply the first-time homebuyer's exception to the gains to avoid the 10% early-distribution penalty on the gains. The returned $6,000 contribution will be treated as never having been made, so it won't be deductible on your tax return, but the returned $6,000 also won't be taxable or subject to any early-distribution penalty, only the gains will be taxable.
Again, it would have been better not to have made the contribution in the first place, but the contribution has already been made.
Of course if you don't actually need the $6,000 from the traditional IRA to make the home purchase, you can just leave it in there and take the deduction.
