Dear Rabbi Kornfeld: On your Answer page, 34b, #10a, you translate the gemara that Rebbe Chanina went up to the attic to pray for Rabban Gamliel's son. In our shiur, it was explained that because of Rebbe Chanina's "gyrations", etc. when he davened, he prayed alone. If he was saying "refa'eynu" in Sh'mone Esray, what about his obligation to pray with a minyan. If not, what tefila was he saying?
The simple understanding is that he was not reciting Shemoneh Esreh, but rather he was saying a private, personal prayer, which one may certainly recite in times of need.
Regarding the issue you raised concerning Davening Shemoneh Esreh without a Minyan, the Poskim discuss whether one is exempt from Davening with a Minyan if he has better Kavanah when he Davens by himself. Rav Moshe Sternbuch, shlit'a, cites the Poskim who write on the issue and elaborates further in his Sefer, "Teshuvos v'Hanhagos," Chelek Alef, Simanim 96-98.