You need to do a bit more research and as @littleadv often wisely advises, consult a professional, in this case a tax layer or CPA. You are not allowed to just pull money out of a property and write off the interest.
From Deducting Mortgage Interest FAQs
If you own rental property and borrow against it to buy a home, the
interest does not qualify as mortgage interest because the loan is not
secured by the home itself. Interest paid on that loan can't be
deducted as a rental expense either, because the funds were not used
for the rental property. The interest expense is actually considered
personal interest, which is no longer deductible.
This is not exactly your situation of course, but it illustrates the restriction that will apply to you.
Elsewhere in the article, it references how, if used for a business, the interest deduction still will not apply to the rental, but to the business via schedule C.
In your case, it's worse, you can never deduct interest used to fund a tax free bond, or to invest in such a tax favored product.
Putting the facts aside, I often use the line "don't let the tax tail wag the investing dog." Borrowing in order to reduce taxes is rarely a wise move. If you look at the interest on the 90K vs 290K, you'll see you are paying, in effect, 5.12% on the extra 200K, due the higher rate on the entire sum. Elsewhere on this board, there are members who would say that given the choice to invest or pay off a 4% mortgage, paying it off is guaranteed, and the wiser thing to do. I think there's a fine line and might not be so quick to pay that loan off, an after-tax 3% cost of borrowing is barely higher than inflation. But to borrow at over 5% to invest in an annuity product whose terms you didn't disclose, does seem right to me. Borrow to invest in the next property? That's another story.