This is a great post OP, I'm in favor of anything that avoids spending $12,000 to replace a transmission however you do it! And far be it from me to criticize any way that works.

I'd try your method if I were still able to crawl under a car anymore, I've seen worse ways. But it does seem a bit of a shame not to use OEM Lexus WS fluid for the entire job especially for the flushing part. Because inevitably a large quantity of the flushing fluid is left behind inside the transmission when you are done so that fluid should probably be OEM transmission fluid too.

The one time I tried to use non-OEM ATF on my 2002 Camry V6, I noticed a difference in transmission performance right away. It lagged during shifts and otherwise just did not feel right. It bothered me enough that I changed the fluid back to OEM type a few days later. Fortunately I'd just done a fluid change not a flush, and changing back to factory fluid was enough to make it run right again. But ever since then I have not used anything but OEM fluid in any of my cars. There are plenty of repair items on a car that don't really require an OEM component, but in my view ATF is not one of them... Doesn't seem worth it just to save a few dollars.