I would imagine that any constraints on JR in DT are self-imposed. Since he and JP are the main (practically exclusive) music composers in the band, the DT sound is whatever they say it is.
JR feels that DT is a certain brand and kind of music, and that is the kind of music he does within the band. There are other things he also likes to play that he doesn't play in DT.
Indeed. I remember Jordan said that he had wrote the intro riff for "When The Water Breaks" but he didn't felt it fit in DT.
This "signature sound" mentality i don't really agree with and care for to be honest, even though on The Astonishing those boundaries were broken quite a bit i think. But it is restraining, and this is why i compared to LTE and the more recent DT albums, where i think both Jordan and JP seem to have stayed within a very certain musical path, even though we know they can do some more jazzy, even fusion-like stuff and they used to do it in the past.