If you want to work in biomed, as long as the drosophila work is focused on neuro, genetics, molecular biology, or other biomedical applications, it should be fine.
The name of the degree doesn’t matter as much as the type of projects you’re doing, and most importantly, your advisor’s work and reputation.
If the drosophila work is focused on a non-biomed topic, I would steer away from that.
If you want a career in biomed, the ASU nutrition science degree doesn’t seem like a good fit because it has a prescribed curriculum with a clinical bent (I went and looked at the requirements).
The A&M entomology program is more flexible, but I think most people taking that are interested in more traditional entomology careers. Which doesn’t seem to be you, but I think you could tailor it to a biomed focus if you really want to.
So it sounds like the LSU program is the best fit for what it seems like you want to do in the future.