This option is bit more involved, and working with pictures makes this hard to determine if it is actually a possible solution. But options and thoughts never hurt. From picture 2, it seems as though the PVC on the smaller side of the tee may be intruding on the drywall space as well? If So a PVC Tee will probably not solve your problem.
I'm not a residential plumber, so I can't comment on the design of the drain. However, if this was my problem to fix I would consider cutting the surrounding galvanized and cast piping to make room for a die-electric fitting or most likely enough brass to braze a copper Tee in line. Copper will give you the most clearance without sacrificing pipe diameter.
That said, galvanized steel must have the zinc coating removed, so if that is a Sch 10 (super thin) pipe, you may not be able to get it clean enough. If you can remove it, maybe you can get it threaded with a coupling to a threaded brass nipple with the threads cut off the other end.
Warning: If you are considering this way please make sure to do your research on copper/steel electrolysis, and galvanized vapors.