If you work through the math, you'll realize that the gain/loss on your active trading capital can be calculated by this formula: (sum of the values of each position as of the last trade in 2017) - (sum of the values of each position as of the last trade in 2016). It doesn't matter how many steps there were, the sum of all the little gains and losses will equal the formula. If you added or removed capital, then you'd have to adjust for that. You also have to adjust if positions move between short and long term holdings.
The IRS forms want to see transaction details, and not just an aggregate total. You'll have to deal with this. However, the intermediate values don't have to be exact - you'll just be entering the same value in a later row. I suppose the intermediate steps could even be reconstructed from your "faulty" memory.
(If in the future you start receiving 1099 forms, then the transactions will need to be listed exactly. Presumably the IRS can check the "total proceeds" number. Usefully though, you don't need to list individual transactions if they've been fully reported to the IRS. Because they already have the details, you can enter their aggregate gain/loss.)
If you have to make variable quarterly estimated payments, then you may need to take four position snapshots a year.