I once had a job where we ordered a large 3" thick Maple island top. When we received the top, it had been shipped in a wooden box wrapped in foam. When we installed the top, the house was still under construction and to protect the top, we put the foam on top of the top and flipped the shipping box on top of it. About a month later, when we took the packing box off, the top had warped. The owner refused to pay for it and I contacted the maker of the top. The fabricator suggested that we wait for a month or two to see if it would come back to the original flatness. It did come back.
I would suggest you wait a longer period of time. I am not too familiar with Beech. I have used it on occasions, I do not recall any problems. The issue with Beech is that you will not be ale to get high grade long lengths. The tree rots in the center and Loggers don't want to waste their time falling them and Mills don't want to take the time to cut it up and the same with the Kilns. It is a cheap wood and the land owner gets nothing for it. Most of the lumber is used in making pallets.
When the major cost in your doors is labor, it probably isn't a good idea to save money on the wood you use.
Also, if you make this door again, you might consider a mortise and tenon mitered corner frame. If your frame comes together at 45 degrees, both the stiles and rails should expand at the same rate.