Big nod to user cas who has been an amazing help thus far for me!

Short background: My grandparents started a taxable stock account for my mother when she was a teenager (from her memory) and it has for the most part remained untouched for decades. I can only find Yahoo historical data back to 1/1/1970 (she would've been 19) so I'm guessing it was not long after then that the account was opened. Until Q2 2012, it had been completely untouched and was setup as a DRIP plan to reinvest all of the dividends into buying more of the stock, which is a single DTE Energy Co. holding (DTE). In 2012 her tax accountant/advisor helped her setup the account to receive the dividends as opposed to reinvest them. Now she is retired and looking to me for help setting up her portfolio, and diversifying this DTE holding which is currently valued at $150k and is making up nearly 1/3 of her total retirement savings is a big part of that equation. With very little to go by in terms of record keeping, I'm having a heck of a tough time figuring out the cost basis and I'd like to get some idea whether this method I'm using to estimate it makes sense.
Other highlights:
- She has records via her online account of the dividend amounts dating back to 2006, so starting here via the spreadsheet below
- She has copies of her tax returns dating back to 2002, so if this methodology makes sense I could probably continue it back through 2002 based on her statements
- No idea what to do beyond that, hoping to figure out a way to estimate, or will be stuck using $0 as the cost basis
Here is a look at what I came up with as a way to estimate the cost basis on the shares that I can find records for. Basically I researched the median share price for the day that her dividend payment was made, and calculated based on that share price and the dividend amount, the number of shares that were purchased. That gave me a total number of shares purchased from 2006-2012, and the total amount it cost to purchase those shares. Then I subtracted the total cost from the total she'd receive today for selling those shares, giving me a value for her net LTCG income from the transaction.
Note: Data in blue was taken from her online account (covered shares). Data in black text is my calculation / estimate.
Questions:
- First of all does this methodology of estimating the cost basis make sense?
- What should I do when the records run out prior to 2006? Is there a mathematical way to extrapolate, or another means of making a reasonable estimate?
- I'm having trouble understanding why when I go to the "sell" section of her online account, I don't see various lots. Everything seems to be lumped together as of (what I assume to be) the date that the funds moved out of the DRIP plan and she set herself up to receive the dividend checks instead. See the image below. Since this is the case, when she goes to sell, how am I supposed to determine which shares are being sold? Do we just get to pick?
Greatly appreciate any help on this!!