How much deeper sink can I get away with without having to redo waste drain?
You've got 3" of trap seal and you are allowed 4" (3" is better) and there is about 1-1/2" of space between the tee and the coupling nut. For a grand total of 2-1/2". You may be able to squeeze more with some reconfiguration but it seems you really need to.

If you need that extra inch you'll need to change the trap to abs and use a rubberized coupling like a Fernco coupling. The abs trap would need to be a hub trap (basically a U shape) with no union. This will allow you to make a 4" trap seal. 

This shows where you can get the full two and a half inches


Hub trap

Hogwart

Instead of using the 90°(street 90) as shown use a section of pipe sufficient to create a 4" trap seal and turn the street 90 around and attach to the wall stub with the rubberized coupling. On the other side (tailpiece side) use a tailpiece adapter and a section of pipe. Done!