I'd go park myself in their office until they get the idea you need it done today. Seriously, Monday may be too late due to the glues used to hold the friction surfaces in place being water soluble.
Tell them you'll take it home and flush it yourself if they can't get to it today. Which is neither difficult nor demanding of any particular expertise.
Reply here for instructions on how to do the flush yourself if decide to do it on your own. Nope you don't need any special equipment.
EdIt: I may not be here so here's an abbreviated how-to...
Your 32RH transmission pumps ATF only in Neutral, not Park, so when you're ready to flush, shift to Neutral. To shut the pump off, shift back to Park.
You're going to have the transmission pump the contaminated ATF+4 into a large bucket or catch basin from the passenger-side port at the bottom of the radiator. That is the output side. Connect a rubber hose with a 3/8" inside diameter to the passenger side port and run that to your catch basin.
While the transmission is pumping the old fluid out into the catch basin, you'll be adding fresh ATF+4 from the top via the transmission's dipstick tube. Insert a small funnel into the tube to help. Just pour fresh ATF+4 (nothing else!) into the funnel in the dipstick tube at about the same rate as the old fluid is pumped out into the basin.
When the fluid pumping into the basin turns bright clear red, you're done, shift back into Park to shut the pump off. Maybe go another quart or two for good measure if you have more unopened bottles of ATF+4.
Check the fluid again once the output hose is reconnected back to the radiator port. Start the engine, shift to Neutral, and use the dipstick to verify it's full or add more ATF+4 until it is. It does not hurt it to be slightly overfilled.
Any brand of ATF+4 is fine, I personally use Valvoline but I wouldn't be afraid to use a store-brand ATF+4 if that's all I could find. Any major brand of ATF+4 will be fine.