162k on original atf fluid??
Only problem now is, there is a possibility that once you start getting good clean fluid in there, your tranny may start to slip and just fall apart.
The fluid in these transmissions NEEDS to be changed every 30k at MOST; chances are you're probably not the original owner and the first owner probably never did the maintenance which could leave you hanging with a pricey bill.
It doesn't hurt to try it; I would definitely do a pan drop/filter replacement over flushing it; flushing it will most certaintly kill it almost immediately.
Your procedure is nearly accurate; except you do not need to fill the pan before reinstalling it. But you DO need to pump in about 3qts into the pan before restarting the truck, or it will suck nothing but air.
Once you have started the truck for proper fluid level check, do NOT shut off the engine until fluid level check is complete, or it will all dump right back out on you.
Also, I would not do another drain/refill within 500 miles, I would wait for at least 2-3k miles to make sure your tranny is shifting good/clear without slippage. You do NOT want too much new fluid in there at one time, remember it's probably this old fluid holding the transmission together at this point....once atf turns black, tranny time is limited basically and I know it sounds weird, but that black fluid is thicker, and although it does need to be changed out....you do not want to freak the transmission out.
Also, I don't know if I would be switching to an expensive atf right away. I would do this first pan drop/filter deal, wait 2-3k miles do it again; then do it again in 3k miles or so....depending on the color of the fluid, you're probably going to need to do it again after that too. You do not need to replace the filter every time though.
FWIW....I currently have 192k miles on the same auto transmission with fluid swaps every 10-15k miles, filter every 30-40k miles, my atf fluid comes out cherry pink to this day. You should always change out the atf before it turns colors....if it can be helped. Sounds like yours was used when you bought it.