Most of what you "know" is incorrect. The third sentence of the first paragraph is mistaken; you don't need to file Form 709 at all.
Any money that you transfer from the US to your NRE account in India is your money and you don't owe any kind of taxes on it; no income tax in India, no gift tax in the US, no Form 709, etc. The money could be whatever you have left from your take-home pay after paying living expenses, or interest income paid by your bank, or capital gains from buying and selling stocks on your lunch hour, or whatever you begged on the streets after work, or the proceeds of a loan that you took out to buy furniture but changed your mind after you got the money, whatever, and any combinations thereof, but there is no tax implication in the US or in India of the act of transferring money from your checking (or savings) account or brokerage account (or whatever you find in your beggar's cup) in the US to your NRE account in India (or an NRO account for that matter). It doesn't matter diddly-squat whether you transfer more than $14K: you are not making a gift to anyone; it is your money and where you choose to keep it is your business. Now, once the money is in India and it starts earning interest, all that interest is taxable income to you in the US, and you must declare it on your US tax return even if you don't get a Form 1099-INT from your bank in India. It is up to you to keep track of your bank balances and record the interest earned. The interest earned in your NRE account is not taxable income to you in India but interest earned in the NRO account is taxable income to you in India. You avoid double taxation of this money by getting a credit for foreign tax that you have paid on your US tax return. If your bank withheld taxes on the interest credited to your account (TDS), you need to take that into account (and refunds of TDS are taxable US income to you).
One other thing to keep in mind is that you have to declare the existence of foreign bank accounts to the IRS on Schedule B of your US tax return except if the total value of all your foreign bank assets did not exceed $10K at any time of the year, the IRS says to answer NO to the question about foreign assets. Remember it is the total value of all assets, not the individual value of each account that matters. Since you plan on transferring more than $14K, this exception will likely not apply to you. You must also separately inform the US Treasury (FBAR report) about the existence of these foreign accounts (here also there is a $10K exception). Search this site for FBAR to read more about this. DO NOT blow off these reports as inconsequential and ignore the obligation to file them; the penalties for failure to comply are severe as many NRIs as well as US citizens of Indian origin discover every year.