Man. I’m sorry to have caused friction here. I thought I understood Pool 101, but clearly ( pardon the pun… ) I do not. I went to the local professional Pool Installer/servicer this morning. I described the issues, and possible solutions. ( Ah ! More puns. )
I have added two elements into the water. I added roughly 1 pound of Lithium Hypochlorite and 2 lbs of [url=“http://www.focuspools.com/products/Omni/Algaecides-MUSTARD-MASTER.asp”]Omni Mustard Master. I’m aware that the amounts exceed recommended volume, the pool will sit untouched for at least 48 hours, then the acidity will be drawn down using basic ph Minus chemicals until it is balanced.
Yes, the pool is a flexible pool with the inflated ring atop it to maintain shape. It did not occur to me that the texturing of that pool made it harder to clean out the algae, and allowed it to grow with greater ease. Drag. 
It was a fairly inexpensive pool, and is a source of much delight around here. Even with the costs of changing the filters every 90 minutes during this cleansing phase, the pool has come in incredibly cheaply for the summer’s use. I just want to beat the algae problem once and for all, if possible so that the next month or so will be fairly mess-free.
I’m still convinced that the rainfall had a lot to do with this… I’ll report back in 24 hours, and then again when I adjust the pH balance in the pool down to a humanely appropriate level.
So, now let’s all get along or nobody gets to jump back into the pool and play Marco Polo !!!