I'd have to look it up, but I have a '97 GL wagon (Vulcan 3.0) and at one point I thought I was going to have to replace my radiator (my original is still in there and I'm about to cross 200,000 miles next week). I thought what I had read (in the Ford Shop Manual) was the front bumper cover had to come off to get at it because it's buried in there out of sight. Taking off the front bumper cover is really pretty easy - just a bunch of bolts across the top, around the light sockets, and a couple kind of hidden a bit on the ends. No special tools required there.
Not sure about my Taurus radiator but I just replaced the radiator on my Impala. It had to be dropped in from the top because the bumpers at the bottom corners had to sit on pegs which were part of the body. I also replaced a radiator on my Mitsubishi and it was the same way. I thought they were ALL this way, no? I know the Taurus has that 10"-wide fiberglass piece that runs across the top from headlight to headlight called the Upper Radiator Support which supports the radiator at the top. Maybe it's just the opposite from most cars: you can slip it out the bottom, then on re-install you just push it back up so it engages with URS?
As far as the tranny lines, if it's like my '97, the lines have the 3/8" plastic ends that you just pinch and pull the line out. Then they should just push back in and 'click' on reinstall (at least, in theory).
I think it's the 5/16" lines that require the tool.