First post - hopefully this isn't too overwhelming. We bought a 1960s era 2 story with full basement back in 2008. My wife is getting tired of lugging laundry (2 kids) up and down two flights of stairs every week, so I'm redoing part of the office area on the first floor to make life easier. When we moved in, we bought a matching set of LG front loaders (electric dryer) which have been great. I've done a little plumbing work in the past (biggest job was replacing the electric water heater in our previous house), but this will be the largest job I've attempted to date. I think I have the basics (including code considerations) in mind but would appreciate any and all feedback. On to the layout:

The room is about 13 x 10.5

A Sketchup rendering of my preliminary plan:

I spent some time this past weekend removing some electrical and the drywall (perfect 4x8 section) and here's what I'm dealing with:

View looking up from the basement - main stack is now on the far right

Wall is double 2x4s to allow room for the HVAC and piping. Main stack on the left is 3" cast iron. The vent stack in the third bay from left is 1.5" galvanized and services all three bathrooms. This wall backs to a full bath. Running the electrical lines for the washer and drier should be easy. Dryer vent will exit to the outside on the left wall. The plumbing I'm not quite sure on.

I'd like to use a Sioux Chief Ox Box or similar to give enough room for the 2" drain for the washer. My thought was to put the supply side in the first bay and the drain in the second and send it over to the galvanized drain. Then I measured it and it's 1.5" at that point. It extends another 8" into the basement and turns 90* to become a 2" drain. Can I replace the lower section of the 1.5" galvanized with 2" PVC to handle the washer or do I need to tap into the 3" stack on the left?

Next, would tapping the copper supply lines with PEX be a problem? I think it would make routing the lines to the washer much easier (plus, new tools are awesome).

I'll be building some sort of platform to both raise the units to a better height (we didn't buy the overpriced pedestals) and incorporate a floor drain that will be piped directly down to the sump pump (just in case).

Last, if I tie the washer and utility sink drains into the 2" PVC (replacing the 1.5" galvanized there now), what does the the height difference between the two have to be? I think I remember reading 6" somewhere?

Thanks for making it this far. If anything is unclear, just ask.