I have a Galaxy Tab 3 (not a phone) with a data plan. My first attempts to stream with it were horrendous, until I bought an app called SoundAbout Pro, which gave me better control of the tablets audio preferences and volume. I wonder if that would help in your case.
I haven't tried tapping off the DR-2d line out while recording before, and didn't realize it was possible until I read your post and tried it out. The level of the line out can be controlled via the OUTPUT toggle switch. I'm not sure about the MONITOR menu settings; a signal is present from the line out when in record/or pause whenthe monitor is set to off, but when it is set to on I get a signal even when not in record mode.
The few times I have streamed via my Tab 3, I have run rca out of a DR-680 (2 mics and mono sbd) into a passive mixer, and out of that (eta: via the adapter linked in my reply below) to the tablet's TRRS input. I will try streaming from a DR-2d tonight (if I get internet where I'm going) and see if I can add more to this conversation.