No, you do not need a new W-2. Instead, what will happen is when you enter your two W-2s with their code G amounts in box 12 (the contributions to your HSAs), TurboTax will add them together to make $4,070.
When you tell TurboTax that you were covered by a Self-only HDHP all year (it does not matter if you changed policies when you changed jobs, so long as they were both HDHP), TurboTax will calculate your annual HSA contribution limit to be 3,600, as you already expect.
Then TurboTax will declare that you have excess contributions of 470 and ask you if you want to withdraw them before April 18th. Since you have already withdrawn it, you will answer "yes".
As soon as TurboTax recognizes that you have made excess contributions, it will add any employer contributions (the ones with code W in box 12(s)) to line 8 of Schedule 1 as Other Income.
This means that you should NOT add this amount as miscellaneous income, because it's already been done (go look at Sch 1, line 8 to see what I mean).
You won't have to pay Social Security tax or Medicare tax on this 470 - the 1040 doesn't have a mechanism to collect it.
So you have probably already done what you need to do.
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