How can I serialize a queryset from an unrelated model as a nested serializer?

You can use DRF's SerializerMethodField.

Define your ResearchTemplateSerializer as a normal ModelSerializer, not as a RelatedField.

Then replace your ResearchSerializer with this:

class ResearchSerializer(serializers.ModelSerializer):
    templates = serializers.SerializerMethodField()

    class Meta:
        model = Research
        fields = ('id', 'created', 'speaker', 'body', 'templates')

    def get_templates(self, obj):
        values = obj.get_values() # whatever your filter values are. obj is the Research instance
        templates = ResearchTemplate.objects.filter(mergefields__contained_by=values) # Or whatever queryset filter
        return ResearchTemplateSerializer(templates, many=True).data