If it has a DEJ with a low throttle position dead spot... what position is the clip in? Try and raise it a few more clips, but if it's raised a lot already you might try changing.
I would buy a DGH and an EEJ and then start experimenting with what works best. Needles are the single most important and most overlooked aspect of the carb. It controls everything in one way or another except for idle, it can also have an affect on WOT as well. If your having a dead lean spot low in the throttle then you either 1) need to raise the needle more, 2) get a smaller diameter needle or 3) get a shorter needle. Well, with a DEJ, you already have the short needle. So, you can get a smaller diameter needle, the DGH which will help mostly from idle to 1/4. The EEJ has more taper and will help richen the 1/4 to 3/4 but mostly from 1/2 to 3/4. They all will affect the other areas a little but it's an experimentation thing with needles, to find one that your bike likes.
If it were me, I'd go straight to the DGH with the smaller diameter and raise the needle up. Again, I'm going to say you'll have some troubles getting dead spots out of the low end due to the lack of vacuum with such a large carb. Your likely to never get it perfect with a 39mm, especially w/o porting.