the crossover pipe just flows exhaust into the other manifold where the turbo is. a leak or broken crossover can harm your mileage by not allowing your turbo to function at it's full potential. most of the piping after the down pipe is straight 2.5" through the soot trap up to the muffler. you should be able to pick up a section of straight 2.5" and a couple of couplers, a few u-bolt clamps. this will allow you to chop the soot trap off and run straight pipe down to just before the muffler.
for low noise level I wouldn't recommend a axle dump, the exhaust resonating from the road will make it loud in the cab. it also can cause cause a bit more exhaust back pressure as the air from the tail pipe flows out and "hits a wall" at the ground. it the pipe is curved out behind the rear tire or piped straight to the back bumper it will flow freer and be quiet.
when I bought my truck, the PO had chopped out about a 12" section of pipe just behind the soot trap leaving it open under the cab. the muffler and tail pipe was all still intact. for the life of me I never figured out why he had cut it there, but I finished it off by removing the soot trap and re-connecting the muffler so it would pass state inspection.
if your going to spend some money on the exhaust, go for the 4" kit. it's fairly easy and straight forward to install. Just get a muffler to quiet down the noise.