I don't think most EM people care about research, so I don't think that's an issue.
If I remember correctly, SLORs can properly only be written by academic EM faculty, that is to say attendings at a residency program. I think the consensus is that it's pretty important to have SLORs from appropriate writers.
I guess I'd try to cast a wider net for aways. I know my [awesome, new] program is very DO friendly but I have no idea what the situation is for med student away rotations. I can try to check if you want.
It sounds like you have some great strengths in your app though. Be careful about saying you didn't get honors because of a technicality; I have no idea what the situation is but some people are very touchy about anything that sounds like externalizing blame for grades. Good luck!