For a) it would appear that if you are eligible for a qualified LSD for NUA purposes, the cost basis would be 3k. However, if the company stock paid dividends that were reinvested into more company shares, those reinvested shares would add to the cost basis. Always get a quote for NUA cost basis before requesting a distribution of the shares to a brokerage account. Once the cost basis exceeds 25%, the value of NUA decreases considerably.
For b), while the math does not appear to be correct, if you purchased 400k of company shares, your cost basis would have increased by 400k for the shares, basically making NUA worthless by diluting your former cost basis. Most plans use average cost basis for NUA shares and not provide separate lot accounting, and that is what the plan is telling you.
If you go ahead with the LSD and your 1099R for the non rolled over portion (company shares) indicates a cost basis you find unacceptable, you would be on very thin ice to attempt to override that 1099R, including filing your own substitute 1099R. A few taxpayers in the past have attempted to distribute only certain lots using their own documentation rather than that of the plan, but those that got away with this can probably be attributed to lack of IRS oversight rather than overt IRS acceptance. Again, since it appears that your distribution of company shares will now have a very high cost basis, you should abandon the idea of NUA.
I doubt that the plan administrator will allow their procedure to be altered in your case unless they did something wrong, but in this case they appear to be following typical NUA accounting procedures, and even if a CPA agreed to report this by your records, they would require that you bear all the risk, underpayment penalties etc, and you would probably not be sleeping too well for many months or even year after filing your return. For underreporting your income by over 25%, the IRS has 6 years to audit you while potential penalties and interest continue to accumulate.

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