You're 100% correct, we lose out to the Ravens in any tiebreaker situation unfortunately. We'd be 2-3 in common games and they'd be 3-2 (vs. MIA, SD, HOU, and CLE). My guess is ESPN's software doesn't include common opponent tiebreakers for all various combinations of teams that could be tied since that would be a huge pain to include.
Simply put, we need 3 of the following 5 things to happen: SD loss, KC loss, CIN 2 losses, PIT 2 losses, BAL 2 losses. When you factor in the head to head matchups of KC-SD (eliminating someone) and CIN-PIT (putting someone in ahead of us), we need 2 of these 3 things to happen: the PIT-CIN loser loses their Week 16 game, the SD-KC winner loses their Week 16 game, or 2 Ravens losses. 2 Ravens losses is by far the least likely scenario.
Fortunately for us, if all "favorites" win their games, we'd get the help we need (we'd need to win our 2 games of course). The favorites currently would be SF over SD, PIT over KC, BAL over HOU, DEN over CIN for this week, then PIT over CIN, KC over SD, BAL over CLE next week. Those results would put us in over CIN, SD, and KC. Based on the various scenarios and the likelihood of each result happening I give us a 29% chance of getting the help we need, which goes up to 40% if SF beats SD and falls to 17% if SD beats SF. The key games are really DEN beating CIN and SF beating SD.