You've got good mics (I presume), and a good preamp, so what you need is something to capture the output from the pre, do the A/D conversion, and store it to memory card/hard drive. There are a ton of different boxes that will fit that need. A quick look at the Safesound audio p-1 documentation says it's got balanced outputs, and a maximum output of +21dBu, which is pretty hot.
I'm sure someone will jump in here and recommend the Sony M10, which is a very good small recorder. It has only unbalanced in, but the Safesound doc seems to imply that's OK. If you really like the idea of a small recorder, it's worth a try, but going balanced > unbalanced and cutting back the gain may be part of the reason you have felt the need to move past the DP004.
The next big question is "how much do you want to spend?"
A lot of "reasonably priced decks" don't take balanced inputs with a hot signal, so you will probably end up turning down the gain on the pre, and watching the meters on the recorder. I'm guessing that's what you did with your Tascam DP-004. I'm trying to think of good recorders with balanced line in, that aren't overly expensive. An Edirol R44 will take that hot signal, just turn the gain all the way down. Those go for about $1000, and record 4 channels, so you could bring in a couple of other mics at the same time if you like. A Sound Devices 702 is a great box, but costs about twice as much as the R44. Many of the other recorders that tapers use have unbalanced line inputs (PMD661/671, HDP2, etc)
If you are used to the paradigm of laying down a couple of tracks, then overdubbing more while listening to the first tracks, that is something that 99% of us here have never done with our gear. How well those features work, we can't really tell you. If that's an important aspect, you'll have to research that.