I was going to say that about the transplant as the pot is as you say bowl shaped!lol!
No drainage is bad in some circumstances, could lead to overwatering which you may have. I dont know if drilling holes in the base or side is that feasable. I have little experience of these situations where the plant didnt suffer a little. Maybe providing a little water often may be better from time to time to allow the soil to dry somewhat and definatly cultivate the top soil and inch or two to help evaporation of moisture from the soil.
Seems you might have problems here, maybe ferts are the answer also, can but try. There is also the option of cracking the pot open to release the roots but it might get messy and stress the plant a lot, no problem if not in flower i guess.
Just my thoughts, looks a big enough pot. Peace