It has been a long time since there was even a vague justification to call myself a Benkö guru. I haven't played it since 20 years or so and haven't kept track systemetically either.
http://www.jeremysilman.com/chess_opng_anlys/Pain_and_Anguish_3.html GM Karel van der Weide agrees that 10...Nb6 11.b3 Bc8 is suspect.
So I have looked in my golden oldies to see if I could find some inspiration. Unfortunately I don't have access to my database for the moment (the cause is rather stupid), so you will have to check yourself if it has been played before.
10...Nb6 11.b3 0-0 (why not?) 12.0-0 (12.Nh4 Ra7 13.Bb2 e6) Bb7 13.e4 e6. This idea of ...e6 stems from Bronstein it seems, though he prepared it with ...Qc7 (maybe ...Qd7) and ...Rae8. Compare Averkin-Bronstein, USSR 1974.
You also may compare Flear-Tregubov with a few games in which White chose a similar setup:
9...Nbd7 10.0-0 0-0 11.Qc2 Qa5
a) 12.Rd1 Rfb8 13.Bd2 Ng4 14.b3 Qa3 15.Rab1 Bc8 16.Na4 Ndf6 17.Ne1 Nxf2 Kakageldyev-Vaganjan, Moscow 1979.
b) 12.Rb1 Rfb8 13.Bd2 Nb6 (Ng4 14.h3 Nge5 15.Nxe5 Nxe5 16.b3 Qa3 17.Bc1 Qa5 equal according to Taimanov; Schwarz also suggests 13...Ne8 and 13...Rb7/14...Rba7) 14.b3 Qa3 15.Bc1 Qa5 16.Rd1 Ne8 17.Bb2 Nc7 18.e4 c4 =(T again) Salzman-Benkö, Lone Pine 1981.
But I suppose that White can do without Qd1-c2. Moreover Black is happy with an early draw here, if White answers ...Qa3 with Bc1.
Another idea is 9...Nbd7 10.Rb1 0-0 11.0-0 Qb6 12.Qc2 (12.Bd2? Bc4!) when Schwarz likes Qb7 13.Bg5 (13.Rd1 Bc4 and 13.Nd2 Rfb8) Bc4 Jakobsen-Westerinen, Linköping 1969.
Hope this helps a bit.
Thanks, dear chessfriend, I missed your generous post. I'll take a look at what your ideas.