Or....If you do all of the above, but keep the time correction tool checked. You can process the pitch shift, then open it in the editor (double click) and click the musical note button (Audio Tempo definition tool) Then on the far left (you may to expand the window pretty far to see it), there is another button with a musical note on it (musical mode). Click that. This locks the event to the tempo of the tune.
Then close the editor down, click 'tempo' on the transporter to set it to 'Track' press ctrl+T to open the tempo track. Set Insert Curve in the drop down box at the top to 'Ramp'
Find the bit where it starts. Click the pencil button, draw a dot on the line where it starts. Make sure to click it so its still at the normal tempo. Then goto where it ends, draw a dot, click the arrow on the toolbar (object selection). Drag the dot down to 0bpm. Click the pencil again. Draw another dot at the normal speed, roughly where you want it to speed back up again (assuming that you do). Click the arrow, drag the dot to exactly the right place where you want it. You make have to screw around with to decide whether you want to a jump or a ramp.
Once you've done all this, with the audio event being locked to the tempo of the track, it will slow down with the tempo.
While I was experimenting with this a few minutes ago, I did notice as the audio slowed down it obviously broke up in that nasty digital audio slowing down way. However I was, as an experiment, slowing down from 200bpm to about 5bpm over a pretty drawn out period.