If you would normally apply for your benefits to start in October, it seems rather silly to worry about the tax. You would be giving up 3 full months of payments. Maybe you would net 70% of the payment after state and federal taxes, but 70% of something is better than 100% of nothing, isn't it?
However, if delaying 3 months will also increase your lifetime payout, that might be a factor in favor of delaying. I don't know how the increased benefit for delaying is calculated. For example, if by delaying, you give up 3 months that would be $5000 of net (after-tax) benefit, but you gain an extra $25 per month for the rest of your life, that will work to your benefit as long as you live to at least age 83.
