Quickie:
All students qualifying under the IDEA (special education) are automatically protected by 504 and ADA (civil rights). You needn't choose protections in that sense.
504 plans provide related aids and services to address individual needs usually related to access to the same curriculum.
IEP (or ARD in Texas) provide related aids and services to address unique educational needs, i.e., special education.
As such the procedural safeguards will vary, as will regulatory authority between the two. The IEP will develop measurable goals and has more robust safeguards including more for parents compared to 504 (but again the student is protected). The school has more leeway in evaluating the student, however.
For food allergy alone I would not recommend it but you won't be sacrificing 504 protections for food allergy if that's the underlying concern. From what you've written it sounds like student really should be evaluated for IDEA eligibility to receive sped services despite placement probably remaining predominantly in general education.
You may have to trigger an IEE if district has predetermined services. A good first step is to get that ST or SLP to commit that evaluation in writing to submit with your request for IDEA eligibility. That and whatever medical diagnoses you have because an educational diagnosis is actually separate from the medical. Yes, I know how strange that sounds.
I'm not an advocate but I know where you can find one if you want.