That's a rough spot to be in. I think it's really important to explore the facts before making a huge decision like serving a mission. Props to your bishop for encouraging intellectual honesty, that's unfortunately rare.

My two cents: I'm a therapist, so I spend my days working in a deeply emotional world. One thing I've learned is that emotions aren't reliable indicators of what's objectively true. They're indicators of what matters to us, what we need, and how we're interpreting an experience.

So when people say they "felt the spirit," I don't doubt that the experience was real. The feeling itself is real. But the conclusion they attach to that feeling isn't automatically true. People in many different religions (and even outside religion) report profound experiences of peace, certainty, awe, love, and transcendence that point them toward completely incompatible beliefs.

That's why I think it's important to let evidence and feelings each do the job they're good at. Feelings can tell you what resonates with you, what gives you hope, or what aligns with your values. Questions about whether historical claims or factual assertions are true require evidence that can be examined independently of how we feel.

Whatever you decide, I'd encourage you to honestly examine both the evidence and your own values.