Any opinions on how to move forward? Specifically how we'd report the sale on our taxes with this info, and/or how we'd chase down accurate cost basis info?
One option I read is to simply play it safe and claim a $0 basis. But then we'd be paying taxes on an apparent $19K gain, whereas the reality is more like $10K. The difference is significant enough to give me pause.
Can we be conservative and claim a basis of $8K (or something in that range) and pay taxes accordingly? Would it be a problem that we don't have any proof?
Also, the fund has been paying dividends monthly and getting reinvested. So when we sell, there will be a portion of shares that were less than 12 months old. Does this imply a part of this will be short term capital gains (pretty small part, but still), while the rest will be long term?
Your cost basis is grandma's initial investment plus the dividends.
What I would do is claim $8900 plus whatever dividends you can substantiate from either 1099-DIV forms or brokerage statements. If you are missing statements from certain periods of time, you could conservatively estimate it by figuring number of shares you had that year times the per share dividend figures from the mutual fund company. You could also ask the brokerage company that held the shares for you during that period to see if they can provide you with the information.
Personally if you have a reason for believing that the initial investment is $8900, I think it is actually more conservative to use the $8900 figure to calculate basis rather than some lower $8000 number. The more things are simple and make sense and you have a justification, the more likely the IRS is to accept your point of view. For establishing the $8900 figure, you could ask grandma or her bank for the original check, or she might have saved bank statements from back then. Since it is related to the gift limit, you could also probably look that up and buttress your argument that way.
Write yourself a note stating how you calculated your basis and file it with your taxes. 99+% of the time the IRS doesn't question it. In the <1% of the time when they do, you share with them how you estimated it. Most of the time, they will likely accept your estimate, especially if you made a reasonable effort to calculate it, which it sounds like you will be doing. If they don't accept it (which could happen although I have never heard of it with an ordinary taxpayer), they may tack on some taxes and interest, but it won't be large and will likely not include any penalties.
Yes, you can always claim $0 basis, but your thinking is correct that you're way overpaying taxes if you do so.
The $15K number when you transferred the shares is irrelevant; that's just the value of the shares as of when they were transferred and has nothing to do with basis. Basis is what you paid for the investment.
As to your last question, yes, the shares that were purchased in the last year will become a short term capital gain or loss when you sell. What you will do is separate the shares into two lots: one short-term capital gain or loss, and one long-term capital gain (<-probably) or loss. The basis for each lot is how much you paid for each set of shares, and the gain is whatever you received per share pro-rated by the number of shares in each lot.