I think it looks like an awesome idea! I don't know anything about drill team really except a few of the basic movements, but I think adding jumping in would be exciting for the team and the audience. I also don't think it would be weird to have western and english as long as everyone was dressed the same. Most non-horse people probably wouldn't even notice
ETA: Some of the lighting in the video you posted would give me a seizure if I was riding there. Haha. Way too much flashing!