Options for a high set P-trap

Hi folks, I would really appreciate some advice on where to go from here.

My situation:
I have recently been redoing many parts of my kitchen, and the cabinets and countertops are all still unattached. We got a new sink that is deeper. I was able to get the fittings to work for a P-trap to go into the current drain pipe (cast iron in the wall, behind lathe and plaster). However, we have also purchased a dishwasher which changes the drain situation again. The dishwasher will be placed across the path from the sink (on the opposite wall, only about 4-5 feet away).

The plan is to run an extended (maybe 12ft) drain hose from the dishwasher, under the floor (easily accessible), back up through the back wall, and into the sink drain system. I don't foresee a problem with the 12ft extension, but the main problem I'm faced with is how to get the dishwasher drain hose before the P-trap. The piece that attaches to the sink is very close to the actual P-trap, so it doesn't seem like there is space to add one of those Y-pieces for the drain hose.

Suggestions? I don't know my way around the plumbing options here very well, so any help is greatly appreciated.

Kind regards,
Matt

Lower the fitting in the wall so that the trap will be low enough to accommodate a dishwasher tailpiece. For a deep sink the fitting in the wall should be 15-17" above the floor. This would also allow you to install a disposer in the future.

Change to a brass sink drain. It should be short enough that the "proper" dishwasher drain fitting will work.

Hi hj,

Do you mean something like this?

Yes, and you will also need a "captive nut dishwasher tailpiece" so you do not need a short piece between the tee and drain which would lower it again.

Thanks AJ and cacher_chick for the help. I'm going to give it a shot this weekend and see what happens.

Have a great weekend all!