You want to perform that service or you want to have it done?
They use a machine with it's own pump.  The only way I could ever think to do that myself would be to pull the trans cooling lines from the radiator and use the transmission's pump by setting the output line to pump into a bucket and feed the input line with a fresh source of trans fluid. Just don't let the pump ever run dry.
I've never tried that, but that's the only way I could figure I could do it.  I ended up taking my other cars for trans service and you're right, they don't want to change the filter.  I'm not sure how any debris in the filter would flow back out as they flush, but that's their story and they stick to it

For the Tracker, I dropped the pan, installed a drain plug, changed the filter, put the pan back on, and topped it off. ÂÂ
That's when the trouble started!  It started slipping badly between shifts and, when cold, would take forever to shift from 1st to 2nd.  I was very lucky to get it resolved by draining off a couple of quarts, shifting through the gears, draining a couple of quarts... etc... etc until I figured I had better than 90% of the fluid changed (there's no way to drain that torque converter except to pump it out, remove and then drain it, or knock a hole in it

-- none that I know of anyway) and it finally started shifting like it should.  If I had more confidence in my 155k trans, I'd go synthetic.  The best way I think you could do that is to get the old stuff pumped out or to try the method I talked about above.  Otherwise, you're going to have synthetic mixed with non-synthetic.  I don't know if that causes any problems in a transmission, but I don't think I'd want to do that.
Post what you decide to do and the results.  Good Luck.