I have never done this but have heard of many 3.8 swaps being done. If you can, see if you can't get a 5.0 out of a 94-95. This way the fitment just sits better. You could take the gauge cluster and wiring harness to match. I have never heard of a 5.0 in a late built 3.8 tho. Just the earlier 94-98 ones. Does it have the electronic or mechanical odometer? I'd say its a littler more easier to do if it has the mechanical odo if you decdie not to go with a 94-95 and pull the gauge cluster. You will need to determine which wire is for what on the cluster wiring harness. That's why I suggested a 94-95 and swap the gauge. What tranny is currently in the 3.8? I know you wont be able to use your current tranny with a 5.0. What I hear is the input shaft on the 3.8 tranny will be too long for the 5.0's output shaft. Maybe find a T5 from another 5.0. I would prefer that against the AOD from that Mercury. AOD's are just troublesome imo. They don't hold up as well as the T5's or C4's.
Have you ever thought of getting a used 4.6 engine instead? Just an idea.
Try asking this up in the 5.0 forum section. There's a hell of a lot of knowledgable motor heads over there that have done many engine swaps. You may have better luck asking there.