Let's walk through the math together.
You currently own 18 shares (after the 10:1 reverse stock split), with an original cost basis of $6,894, in total. Therefore, $6,894 divided by 18 = $383 per share. Hence, your per share basis, which you would use to determine gain or loss for tax purposes if you sell, is $383 a share. In other words, your total cost basis in the stock remains unchanged after the stock split; it is simply spread over one-tenth the number of new shares.
If you've had reinvested dividends over the years, then, technically speaking, any and all of those fractional shares that were reinvested from dividends have a specific, and identifiable, cost basis. The basis of each reinvested share would equal the amount of the dividend(s) paid out by the company (and on which the stockholder presumably paid income taxes), for each period and for each fractional share. Figuring these numbers out, for a stock that paid quarterly dividends over 40-years would involve looking up historical stock prices for that security on 40 x 4 = 160 different dates over the last 4 decades! That's certainly a monumental task, and probably not a necessary one.
Before the IRS rules of recent years, some brokerages were "sloppy" in their cost basis recordkeeping, especially where the equity account owner had a basic kind of account, or didn't subscribe to an upgraded account service plan. (In the current language of the industry, stocks are considered "covered" if they carry mandatory basis reporting, and "uncovered" if they don't; all new common stock purchases going forward are "covered" securities).
Thus, with your 40-year long position in this equity security, it is most definitely "uncovered." Therefore, you will need to use your best judgment and your own calculations to determine the cost basis, for when and if you ever sell the shares. If you use any reasonable determination method, the IRS should accept this. If you've kept a spreadsheet along the way, for your dividend reinvestments, then that's all the better.
Thanks for asking this thoughtful question.
