[typed while you guys were posting, throwing it out there anyway]
Hey Trey,
I also run a R-44 (Oade mod) and am very happy with it. It's a solid machine and I have no reservations at all recommending one. It's simple, relatively rugged and just plain works without worry in any condition I've used it in. I can't speak for the quality of the stock preamps since I bought mine from Oade pre-modded and don't feel I usually need an external preamp. I do use a V3 sometimes but rarely into the R-44 simply because I didn't feel I gain enough from doing so and can keep the rig small and tight without the external preamp. Like 'galoot I use 9V DVD batteries with a reversed polarity connection cable at the recorder end- sleeve positive, center pin is ground.
I ran 8 channels last night into my DR-680 (it's not modded) by inputting two channels digitally from the V3. That's 6 channels through the onbard 680 preamps + 2 digital in from the V3. I'm also very happy with the DR-680 and really dig having the ability to record 8 synced channels in one small, inexpensive machine. It's menus and operation is more complex than the R-44, the switches on top can be more easily accidentally knocked and there is the well known powering related problems some have had with them when using other than the recommended voltage for outboard power. I've had no problems with mine, and can recommend it for those who need 6 or 8 channels on limited budget, but it isn't as simple and fool proof as the R-44. Stock preamps are fine and quiet enough, and seem more or less on par with those in the Oade modded R-44, though I haven't compared the two critically.
I haven't used the Tascam HS-P82, but it looks like a somewhat more professionally oriented machine positioned to be less costly than SoundDevices, Nagra, and the ohter big players. If you need 8 channels regularly, that may be the more attractive option.
I think it really comes down to how many channels you want/neeed.