Minyan with a deadline

Since the majority of the undergrads have left campus, minyanim have been sort of spotty. Today for shacharis, we had 8 by the end of pesukei d'zimra and managed to get 10 by making phone calls, except that the delay caused us to approach a deadline at which one of the original members had to leave. In order to avoid losing our minyan before leining, the gabbai announced that we should skip the V'hu Rachum section of Tachanan, and move directly into nefilas apayim.

Was this the proper move to make, or would we have been better off saying the full Tachanun and potentially not having a minyan for leining?

Perhaps it would have been proper to say V'hu Rachum after davening?