Well, the corrected Form 1099-R isn't really any worse since the original is worse than I suspected.
Code 02 (actually just code 2, there is no zero code) makes no sense for any distribution from IRA that includes tax withholding; code 2 is really only used by IRA custodians to report Roth conversions. It seems that they processed this as if it was an indirect rollover and should have used code 1, not code 2, to indicate that.
A code G From 1099-R is not permitted to show any tax withholding. Code G indicates a direct rollover, meaning that the entire gross amount went directly to the receiving account.
I assume that there was no state tax withholding. What they need to do is to correct the code G Form 1099-R again to show in box 1 just the amount that was directly rolled over to the 401(k) and should have zeros in boxes 2a and for the tax withholding. The tax withholding must be reported on a separate code 1 Form 1099-R in boxes 1, 2a and 4.
Because of this financial institution error, you should be able to self-certify that you would qualify for a waiver of the 60-day rollover deadline due to financial institution error, allowing you to roll over the amount withheld for taxes to continue to defer taxes on that portion and to avoid the early-distribution penalty. You'll have to come up with the funds to complete that rollover and you'll recover those funds as part of your tax refund or reduction in balance due when you indicate on your tax return that the amount of the tax withholding was rolled over.
I would find a different IRA custodian for doing your new traditional IRA contributions and Roth conversions. This one is clearly incompetent. Sounds like a bank; banks rarely adequately train their employees regarding IRA transactions. I've had mistakes made by nearly every bank IRA custodian I've ever dealt with.
