Using double faced tape to hold a plate or platter on the lathe while turning sure seems like it wouldn't work very well but I have been doing this for many years and it has worked well. Here's how.
Plane or joint your blank so it is smooth on both sides. Mark a circle and cut out a round blank with your band saw but be sure to mark where the center of the circle is.
Screw the combination on the drive and then give it a bit of a spin to see how close to centered it is. It really isn't critical on this side, but you'll do it again for the other side and it will be very critical then so this is good practice. Bring the tailstock and the live center up to the blank and seat it against the wood.
Let's put a footnote in here -- when you turn anything on the lathe, you are applying force to the wood with your cutting tool. The farther you are cutting from the center of the piece, the more leverage you have against the chuck. If the piece is not well held, a catch or aggressive cutting could dislodge it from the chucking system you are using. When you have the tailstock up against the bottom of the blank, you can cut confidently as it is highly unlikely that you will dislodge the piece from your chuck, in this case the double faced tape on the faceplate. However, when you back off the tailstock to trim off that little peg in the center, the only thing holding the wood in place is the tape. Cutting aggressively out away from the center of the piece and/or getting a catch out there may jerk the piece free of the tape so when the tailstock is backed off, cut gently. Also, when you are cutting that peg in the middle, the leverage you have against your "tape chuck" will be minimal but you should still make light cuts.
Once you have backed the tailstock away and trimmed off the peg, take great pains to make the bottom of your platter as flat as you can. Use a straight edge of some kind to judge flatness and trim as needed. The reason it must be so flat is that you will retape the faceplate and apply it to the bottom of the piece next and the flatter it is, the better the tape will adhere. Sand the bottom but be careful that you don't unflatten it by sanding too much in one spot.
IMPORTANT: Once it is really flat and before you remove it from the faceplate, make a small mark at the center with a pencil and then measure out 3" and mark a 6" circle on the bottom. That will be your target when you turn it around.
Pry the blank off the faceplate. Remove and discard the double faced tape strips. Test-fit that faceplate inside the 6" circle on the bottom of the platter. If you can't see the pencil line, use a compass to lightly mark another line slightly farther out and test fit the faceplate again. When you know how the faceplate compares to that new circle, apply two strips of tape as before. As you gently lay the faceplate within the circle, orient the grain of the wood with the direction of those two strips of tape. I'll explain why in a minute. Once centered, set it on the floor and stand on it again. Screw it on the headstock drive.
Time to remove the finished platter from the faceplate. Orient the grain of the piece parallel to the floor. It may help to lock the headstock in position. Push or pull at the end of the platter closest to you, which should be end grain, to slowly unstick it from the tape. It may be helpful to slide something thin between the faceplate and platter in the center of the faceplate between those two strips of tape. I use one of my wife's kitchen knives. She was a bit surprised when she saw that I had it in my tool bucket. If you have made your platter too thin and are pulling somewhere other than at the end grain, you could break the platter. By orienting it so the grain is parallel with the strips of tape, when you pull away from the faceplate, you can pull pretty hard without concern about breaking the piece.
As always, I highly recommend signing your work. I use a vibrating engraver to write my name, the month and year, and the type of wood on the bottom. Depending on the wood, an engraver like that may leave a rough surface. Lightly sanding with 400 grit will smooth that out. Then finish the piece with your favorite varnish or other finish and enjoy.