Framcus, welcome to the forum! Your and Richard's discussion went a little over my head, but I'll try to offer some practical advice
Since the shape of the pool (and it's bottom) precludes a 'plug and chug' number, do what we pool dudes have been doing since the first pool was built - guestimate. Run the numbers with your best guess as to depths and areas and get a good approximation of the gallonage, then use 'trial and error' to make chem adjustments (and follow the first rule of pool dosing: "add less than what you think you need" - you can always add more to get where you want). Also, please keep in mind that there is a fairly forgiving range of 'acceptable (optimal) levels' for the various parameters of pool chemistry - use your guestimate as a starting point and, through keeping a journal, adjust the suspected gallonage accordingly.
While it would be more satisfying to KNOW the exact gallonage of the pool, sometimes you just need to be satisfied in knowing that 5 lbs of baking soda will raise your total alk 10 ppm. Don't loose track of the fact that the end result; having water that is clear, sanitary, not gonna hurt the pool nor equipment and a swimmable, hastle-free pool, is what's really important!!
Again, welcome to the forum - I suspect that you'll be a great source of knowledge, though I shudder to think about the headache I'll get if you, Richard, Evan, Steven, Pat, Michael & the rest all post on one thread