If the sink is centered, then I agree that having the trap adapter within one u-bend c-t-c diameter of center simplifies the under sink plumbing. Have you look at rotating the san-tee and just using a 45?
I don't know what code was in force when your house was built, but I glanced at the relevant portion of the 2003 IPC and it appears to be the same as currently. There's also another violation, of 406.2, which says that when the laundry standpipe drain joins another drain, the combined drain needs to be 3". That's also in the 2003 IPC.
Basically. The top two san-tees can use the vent above, but the 3rd (bottom) fixture needs a separate vent. That could be an AAV, or it could just be a revent in the wall.
The tricky thing is how to do the revent without having pipes cross over each other in the wall. If you are going to redo the stacked san-tees anyway, you could do this: The laundry standpipe looks very long, so it could be shortened, so that the laundry connects to the middle san-tee. Then the bottom san-tee side entry, going up stream, hits a LT90, a san-tee for the laundry sink, and the revent rises and joins the stack at 6" above all 3 fixture flood rims.
Instead of a san-tee and LT90 at the bottom, you could use a wye and a 45, but that would require a diagonal hole in the stud. Also, if you really want the laundry sink stub out to be right next to the stud, you could put the LT90 on the right side of that stud bay, having your san-tee point to the left, and then put your stub-out where you want it. Or as I mentioned, turn the san-tee 45 degrees and use a 45, with the LT90 on the left side of the bay.
Cheers, Wayne