Just so we're clear, there are, of course, no penalties for converting to the LDS Church. I assume given context that in your last sentence you meant to say "...would becoming an Episcopalian..." or "...would converting from the LDS Church..." In which case, yes. Leaving the Church will result in a loss of good honor code standing. There is no way around this. One of three things will happen if you chose to become Episcopalian.
The first possibility is that your bishop finds out and decides to contact the Honor Code Office to withdraw his endorsement. In this case, your registration and student status would be canceled immediately. If you live on campus, you would be served with an eviction notice, which would give you seventy-two hours to vacate the premises. If you live off campus, you might have more time. Technically you should be evicted as soon as you lose good honor code standing, but not every landlord constantly checks, and my understanding is that the honor code office is not always super aggressive about contacting landlords. If you chose to transfer to another school, your BYU transcript will indicate that you were dismissed for a violation of the university honor code. Other students who have gone through this process have complained that this notation is often interpreted by other universities as a notice of academic dishonesty, and this prevents them from getting accepted at other schools. However, contrary to popular rumors, BYU is not permitted to withhold your transcripts if you leave the Church.
The second possibility is that your bishop will not immediately contact the honor code office to withdraw his endorsement, but will refuse to issue you a new one if you haven't changed your mind by the time you need to renew your endorsement. You can check MyMap to see when your current endorsement will expire. In most cases, your endorsement will likely expire during the coming fall semester. You won't be able to register for classes or sign a contract for on or off-campus student housing after that time. Like before, your transcript will receive the same notation about a violation of the University honor code, though when that notice is added depends on how quickly the Honor Code office figures out what happened, and I'm not sure how long that takes.
The third possibility is that you convert, tell no one, continue to attend your home ward in addition to Episcopalian services, and live in fear that your bishop finds out. I do not recommend this option.
Here's what I do recommend: Although I think BYU's policy about this is wrong and poorly implemented, at the end of the day I am a member of the Church of Jesus Christ of Latter-day Saints, and I believe that this is the only Church that contains the fullness of the Gospel of Jesus Christ. Trust me, I (and nearly everyone on this campus), have had many days where a Church meeting didn't "click" for me. In fact, that's probably a bit of an understatement. If I'm being totally honest, I've had plenty of days where I've walked out of a particular Church meeting thinking: "Seriously, this is just the worst."
So why stick with it? Let me tell you why I do. I have found that the Book of Mormon is true. It just is. There's simply no way around it for me. So before you make the decision to leave the Church and become Episcopalian, I urge you to reread the Book of Mormon. Switching your religious affiliation is a big choice, and you owe it to yourself and whatever feelings compelled you to join this Church in the first place to reread the Book of Mormon, "ponder in [your] heart the message it contains, and then to ask God, the Eternal Father, in the name of Christ if the book is true." (Introduction to the Book of Mormon) If the Book of Mormon is true, then the Church of Jesus Christ of Latter-day Saints is the only Church authorized to provide the saving ordinances necessary for salvation. That does not mean that there won't be days that it fails to "click" for you. It doesn't mean that there won't be days you want to burn down the building. It does mean, however, that at those times you can fall back on your purpose, remind yourself why you're here, and let those things bother you less.
All this having been said, if you choose to convert to another faith, here are the steps (in order) you should follow to protect yourself.
1. Begin thinking about and applying to other universities. Keep in mind that you'll want to do this relatively quickly. The longer you wait, the harder it is to transfer. You'll have a harder time getting credit for the work you've done when you try to transfer your credits to another school, and its typically difficult to get admitted to another University if you're close to receiving your degree at your original school.
2. Find out if you will need to retake the ACT or SAT. (Most schools will exempt you if you have a certain number of college credits, but the number of credits you need varies for each school.) Do not explain to professors, ward members, or anyone else that you are leaving or why you are. Make sure transcripts are sent promptly.
3. Continue to enroll for classes normally and do well. Register for classes in future semesters as registration becomes available, even if you do not plan on attending. Do not tell anyone that you are applying to other universities or explain why. (You will, of course, need to tell BYU to send transcripts to other schools.)
4. Only once you have received and accepted an admissions offer from another school should you cancel your registration for future semesters. Do not mention that you are transferring unless asked. Do not explain why to anyone until you have completed step four. Continue and complete the current semester. (You don't have to, I guess, but it makes the most sense.)
5. Terminate or sell all your housing contracts for both on-campus housing and BYU-approved off-campus housing. Move into housing that is not "BYU Approved." This protects you from eviction.
6. Formally convert to another faith and share this information with whoever you want.
Let me mention once more that it is not unusual for any member of this Church - or any Church for that matter - to have days where things don't "click" for them. I promise. You're not alone. On the contrary, I think we were meant to have experiences and days where things don't perfectly "click." We're meant to learn and grow, and that involves being presented with experiences and situations that are challenging or don't immediately fit into our understanding. This is one of the primary purposes of our mortal experience.
I urge you to reread the Book of Mormon and prayerfully consider your options before you make any decision.