Here is a suggestion:
Review the first chapter of the Book of Daniel. The intervention was Daniel and his fellow Jewish slaves eating seeds; the control was the non-Jewish slaves eating meat. It is actually the first recorded example of a control group in history; the second would not be until the scurvy experiments in the mid-18th century. You could re-do Daniel’s experiment except that if the study participants are Jews, you’d have to use kosher rather than non-kosher meat: Half your volunteers would be vegetarian for ten days and half would be meat eaters. A stronger experiment would be if you randomly assigned your volunteers via a coin toss to the vegetarian or meat group. Define before the study what you would call “healthier”: Get some independent panel to evaluate the volunteers. Maybe you could also have a nurse or doctor take the blood pressure of the participants. Then let us know the results!