You should do great with the RP in there. Might want to get some auto RXand throw it in and run around for about a thousand or so miles before you do the change to get the seals ready. IF you are about to drop a fortune in fluid, I would hate to see you drop it on the ground.
No fancy $2500 transtech machine needed to flush it out. Drop the pan and change the internal filter, do whatever external filter adding you are going to do. Remove the return line where it comes out of the rad cooler or last coolers section before returning to the tranny and attach a nice length of hose to it. Find a 5 gal bucket and measure off 1 gal increments in the bucket. From here you will need a helper or have to be quick on your feet. Poke the end of the aforementioned hose into the bucket and top off the tranny with fresh fluid and have someone crank the engine , watch the fluid level in the bucket and have them stop the thing when it hits the 1 gal mark. Top off the fluid in the tranny, crank the engine again till it hits the 2 gal mark, stop again, etc, keep repeting this process till the fluid running out the return line is clean new fluid. You have then flushed out the whole box including the torque converter

You will need to have much more fluid on hand than just the capacity of the tranny since some of it is going to be lost to flushing, but considering that you are saving the price of the service and you will actually be getting ALL your expensive RP in there instead of it getting mixed all up with regular dino fluid which is what would end up happening if you took it to a shop with a transtech machine