Its only August. If you can secure a rotation in EM and get one SLOE, you'll have a chance. Is it a perfect application to have one SLOE? Nope. But some PDs will overlook it since you are a late convert. We ranked a candidate near the top of our list who rotated with us late in the game, who had no SLOEs, who was a late convert from ortho. He was excellent on rotation, and was an absolutely stellar resident. He's now one of our faculty. My point is, if you can weasel your way into a rotation by October or November, you at least have a shot because if you are really good clinically, it only takes one program to rank you highly to match.
If you can't, and EM is off the table for your PGY1, you could do a transitional year. It will get hard to get SLOEs from that year, but you could do EM rotations near the end of your 4th year (much easier to secure) and ask them to write you a SLOE for the following year.
If I were you, I'd see if there is any way at all of changing a month in Sept-Nov from one of your Psych AIs to an EM AI. If its a late one (Oct/Nov) you may not get a ton of interviews until that first SLOE comes in. As soon as it does, I'd be hitting up programs you think you may have a shot at via email to explain your situation and inquire about interviews should anyone cancel late in the season. This, combined with applying to some transitional programs in the match is the way I would go personally.