I really can't give you any specific advice because I just don't know enough about your particular situation. However, what I will tell you is what I know about SS results. According to their own published data, the approval rates for SSDI are much higher and happen much quicker for mental type issues (which depression is one of) than physical issues, including serious aliments.
The reason for this is pretty simple actually....With physical aliments, accommodations can quite often be made for many people, and unless they are on a lot of meds and the meds cause other issues (like sleepiness, irritability, a drugged feeling & etc.), it's much tougher to prove that one can't do something that they are reasonably trained for. Also, the less education one has, the more they are "reasonably trained for", which means more possibilities.
However, with mental issues, finding stable employment is often much harder, if not impossible. People with serious mental problems often have many issues which prevent employment...Everything from cognitive impairment, to not getting along with others, to mania/depressive phases. I'm not saying everyone falls into these categories, but rather of the two, the mental side is much more approval friendly.
So, it sounds to me that you've possibly got a case on both sides, which would seem to me, to at least help your overall cause. I'm not sure I would delay anything only because that may put you that much further behind....It's a long process already. Additionally, those with multiple issues are approved more quickly and in higher %s, than those with one issue.
Hope this makes sense.
Regards,
Ex