It used to be that you could use the Series EE proceeds to buy Series HH savings bonds and continue the tax deferral on the principal. You could pay federal income tax on interest income from the Series HH savings bonds in the year it was earned. That ended when the U.S. Treasury stopped issuing Series HH savings bonds in August 2004.
Rolling over into new Series EE savings bonds or gifting them won't help you. Deferred taxes become due in the year that the bonds are redeemed or mature. Gifting doesn't mean you avoid the taxes either.
Unfortunately, I don't think the mortgage interest deduction will be much help either. Borrowing to buy a house may reduce your taxes, including your marginal federal income tax rate. You'd also likely pay a big price in closing costs and mortgage interest expense.
It might be possible to transfer the bonds into a revocable trust without triggering a tax bill. But that also seems less than attractive. Aside from the costs of setting up and administering the trust, you'll face tax bills due as the savings bonds mature.
For savings bonds issued after 1989, you could investigate the Education Tax Exclusion for qualified education expenses for you, your spouse or a dependent, if any of those apply. Since you mentioned the bonds are maturing over the next three to four years, this doesn't seem to be a likely solution for tax savings.
You didn't have to defer the federal income tax; you apparently chose to do so. You could make a one-time change allowing you to pay income taxes annually, but this late you'd still have a big tax bill the first year.
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