Well then you don't need a pad, thats for sure, sounds like you have a handle on the gain staging, I guess the mic could be overloading, have her back off the mic another foot. Other then that not sure why you would be experiencing what you are experiencing. But I am afraid that adding another pre clean/dirty,tube/solid state is just gonna run you back to where you are. Oh its worth a try though, give the Rane or DMP3 a try, take it back if you have the same problems.
You have the same problems with your VTB-1 and SPL? eerrrr, I just reread that you have only tried the SPL on her. Well you have a VTB-1 try it, I haven't had problems like that with mine, but I haven't had a chance to record an Aretha style singer yet. But the recordings I have done with the VTB-1, some of which not all, I have had the tube blend all the way off and it did seem clean enough for a clean vocal that I was going after. You should also try a different input on your sound card just in case one of them is knakered.