Trills in Rachmaninoff Etude 33/2

[peterl]

I just started studying this one.  My teacher indicated I that in the last few measures I should pause each trill, play the broken chord with both hands (with pedal), and then start the next trill.  However in the three recordings I checked (Idil Biret, Helène Grimaud, Nikolai Lugansky) I hear one trill moving directly into the next without a break.  Presumably they are playing the trills with 45 and the RH portion of the chords with 123.

How accepted is my teacher's suggestion?  How do you finger these trills and chords?