I wonder how closely you have studied 2 Peter 3? I tend to think not very. What is "His promise" that Peter said the new heavens and new earth will fulfill? Let's take a look at the text and find out.
2 Peter 3:3 Knowing this first, that there shall come in the last days scoffers, walking after their own lusts, 4 And saying, Where is the promise of his coming? for since the fathers fell asleep, all things continue as they were from the beginning of the creation. 5 For this they willingly are ignorant of, that by the word of God the heavens were of old, and the earth standing out of the water and in the water: 6 Whereby the world that then was, being overflowed with water, perished: 7 But the heavens and the earth, which are now, by the same word are kept in store, reserved unto fire against the day of judgment and perdition of ungodly men.
Can you see here that Peter talked about scoffers in the last days scoffing at the idea of Christ's second coming by asking sarcastically "Where is the promise of his coming"? Peter indicates that they will not get away with their scoffing unscathed because he indicated, in relation to Christ's second coming, that just as in Noah's day "the world that then was, being overflowed with water, perished", at Christ's second coming "the heavens and the earth, which are now, by the same word are kept in store, reserved unto fire".
Then Peter continued and said this:
2 Peter 3:8 But, beloved, be not ignorant of this one thing, that one day is with the Lord as a thousand years, and a thousand years as one day. 9 The Lord is not slack concerning his promise, as some men count slackness; but is longsuffering to us-ward, not willing that any should perish, but that all should come to repentance.
So, Peter points out that the Lord is not being slow to fulfill the promise of His second coming as some imagine. From His perspective, He is not being slow at all because a day and a thousand years are no different to Him. Which makes sense since He created time. Time has no affect on Him. So, He is not being slow in fulfilling the promise of His second coming.
Then Peter said this:
10 But the day of the Lord will come as a thief in the night; in the which the heavens shall pass away with a great noise, and the elements shall melt with fervent heat, the earth also and the works that are therein shall be burned up. 11 Seeing then that all these things shall be dissolved, what manner of persons ought ye to be in all holy conversation and godliness, 12 Looking for and hasting unto the coming of the day of God, wherein the heavens being on fire shall be dissolved, and the elements shall melt with fervent heat?
He describes the day of the Lord as coming unexpectedly like a thief in the night, just as Jesus said about the day He returns (Matt 24:42-44, Rev 16:15). And he indicates that it will be accompanied by the burning up of the heavens and the earth.
Then Peter said this:
13 Nevertheless we, according to his promise, look for new heavens and a new earth, wherein dwelleth righteousness.
So, he was saying here that despite the global destruction that will occur upon the arrival of the day of the Lord (the day Christ returns), we, in accordance with (in fulfillment of) his promise of coming again, are looking forward to the new heavens and new earth where righteousness will dwell.
So, Peter describes the new heavens and new earth as being something directly associated with the fulfillment of "his promise", which as we see from 2 Peter 3:4 is a reference to the promise of His second coming. That places the ushering in of the new heavens and new earth at His second coming and not 1000+ years later.
I see what you are saying however Peter is not saying that. He is saying that in the Day of the Lord, (time period) the heavens and earth will melt etc. That fire is reserved until the day of judgement.
You will need many more scriptures to back up your view of it all happening when the Lord comes.