You said you occasionally eat eggs, tuna and cheese - how are they any different from red meat? I personally don't see the difference. They are all animal flesh.
I'm not saying you should or shouldn't eat it, just asked what, in your opinion, is the difference? I sure don't think beef is any worse than cheese or tuna.
Curezoners should have some good suggestions for you, though. You should be able to figure out a workable solution here.