Some of us get the wrong idea when it comes across as asking for advice even though the person is going to do it no matter what the answer is. I apologize for any hostility but I stand by what I said about it not being the best idea if you're just learning harder cuts, but i'll lay out how I've done it below.
I'm glad you aren't going to cut the Trachyphyllia, and I mentioned the tool I would use to cut the Lobactis. I'd use a wet diamond band saw, the one by Gryphon. I don't really trust the Dremel too much as one's I've used tend to get too hot. I work at a conservation facility, my career is dedicated to trying to preserve the oceans so of course I've thought about it. Those species just aren't exactly the best ones to be trying. The success rate is so so.
But, If you're going to, then cut the plate in half or into several pie shapes. After cutting you'll need to give it a dip to minimize infection. I'd recommend an iodine dip, regular reef dip should work. After dip have a bath of tank water to rinse them in as they produce a lot of mucus and you want as little of that in your system as possible. Once you've done that place them back in your system in a flow area that isn't too strong but enough to carry mucous away, and where they aren't getting blasted by full light or getting buried by sand. After that you have a waiting game to see if they start healing or if they'll get infected and die of tissue necrosis. If they start that then you can give them another dip to disinfect it again, up to a double dose if needed. Once it looks like the mouth has healed you should start feeding immediately. Mysis, plankton, they like fauna marin LPS pellets too.
That's the way I would cut it and start the healing process. After that it will just be a long wait of regrowth and keeping your system stable. That would be my method, others may chime in with theirs.
