As your rabbi said, the halachic custom is to refrain from affixing mezuzot on both posts in a doubtful situation as this may be considered “adding on” to the mitzvot. However, though this is the custom, your question is spot on, and many authorities have addressed it. In fact, some of them have asserted that there is no problem with affixing two mezuzot. Nevertheless, for whatever reason, the fact remains that many of our rabbis have reported that they have never heard that your solution was implemented.
If indeed there is no clear objective criteria to help you choose one post over the other, you may use your subjective judgement and place the mezuzah on the right post of a door you deem to be more logically an entrance rather than an exit. 
 Mezuzot Beitecha, Sh’ar HaTziun 289:45, citing Chazon Ish. Maharam Shik, cited in Binyan Tzion 100; Agur B’Ohalecha 15:4.
 Binyan Tzion 100.
 Daas Kedoshim 286:25; Shevet HaLevi 2:152:1; Minchas Yitzchak 1:9.
 Shevet HaLevi 2:152; Agur B’ohalecha 27:36. One should not recite a berachah on this placement. Cf. Igros Moshe Y.D. 1:176, who exempts this doorway completely.