Depending on what Dead tunes you're performing, you actually CAN play them like a traditional bassist and they'll still sound great.
He's not really dissimilar from James Jamerson on many songs (during the songs themselves) through the 70s.
A BIG Phil thing is to save the low notes. Perhaps as a rule of thumb, try to keep things above the open A string, and keep your duration of each note short. There's very much a space between every note Phil plays. Beyond that, have fun with it, and don't overthink it.