Welcome to my world. First, replace your strings. Then, start with just one mic. You'll probably use two later, but you need to walk before you can run. If you can't make one mic sound good, two won't help. Start with the mic about 8" from the 12th fret, pointed at the 12th fret, not the soundhole. Then record short sections, the same part, moving the mic up and down the neck. As the mic mooves toward the body of the guitar, it will get darker, boomier. As it moves away from the body, it will get brighter. Try this with the DMP-3's Hi/Lo switch in both positions. Adjust the input gain on the tape machine to around the middle and then the gain control on the DMP-3 until the needles on the tape machine get close to 0, but rarely go into the red. Then, play around with the two gain controls, the preamp and the tape machine. Try more preamp and less tape machine, and then the reverse, and see how the sound changes.
Also, get some RCA to XLR patch cables, and pull a Left and Right line off of a stereo source, such as your home stereo, into the reel to reel, and see what it sounds like, with a recording you know very well. That dials your room out of the equation and verifies that your reel to reel is working OK. There are a number of possible maintenance issues that could make a tape machine sound like that, and you need to rule them out. I wouldn't pay too much attention to the vu meters on the DMP-3, but you want to know what the ones on the tape machine are doing.
For right now, you are not trying to track a Grammy winner, so sit and play where you can reach all the controls and see all the indicators. Use headphones to give you some insight into what the tape machine is hearing, and mute the monitors to avoid feedback and phase distortion. Frankly, what you have described sounds a lot like phase distortion, with the signals from the two mics hitting the tape deck at two different times, out of phase just enough to cause trouble. But that is just one of many possible issues, and it may be you have more than one problem.
Can the room make or break a recording? Yes, absolutely. But it isn't the first place I would start for trouble shooting your problem. I admit, I would start at the tape machine, the source, mic placement, and gain staging. If I was sure there was no problem there, then I'd start working on the room. Getting good acoustic sound is the first great recording Holy Grail. Best of luck.-Richie