Could you check whether the multiple gene models mapping to the same gene are just different transcript (alternatively transcribed) forms from the same gene? I image because you're mapping to a closely related species, you probably don't have a reference for your transcripts/gene models, and you probably got them from de novo assemblies of transcriptomes. I'd suggest to do a more rigorous clean-up of your assembled transcriptomes, with a process similar as EST clustering. Then I'd suggest to use gmap or BLAT to anchor them to the closely related species. This could also be tricky, as a lot of parameters are dependent on how closely they are related phylogenetically.