Right off the bat, I hear the sound of a piezo pickup: I recently added a Yamaha APX500II to my guitar collection, and it sounds exactly like this when it's plugged in. Piezo pickups are very common these days, especially on acoustics
I am guessing that Travis is initially tuned to 1/2 Step Down Double-Dropped D (low-to-high: Db-Ab-Db-Gb-Bb-Db).
The sound is fairly straight-forward, but I would bet there is a hint of chorus and compression.
Now as far as your issues are concerned, I am thinking that it has to do with a combination of that particular Marshall you are using and the fact that your acoustic may not have a piezo built in. If I had to pick the most important element of Travis's sound, and the sound you are looking for, I would go with the piezo. Again, I recognized its unmistakable tonal qualities the instant Travis started playing.
Hope this helps!