There are no Puzzle Rush ratings, only best scores.
As for your Puzzles rating (which has a lot more time available) it's not so different to the comparison between my blitz and puzzles. [EDIT: I see your 3 and 4 minute puzzle rush best could be improved. Also you should be able to get a much better survival score, if you have a 2400 puzzles rating!]
is my puzzle rush rating good for my blitz rating, my puzzle one is close to 2400 and my blitz rating is 1650