I have an old house with 2-panel doors throughout, that have the classic ogee style bead.
I would like to make a few more without a lot of trouble and expense.

Rail-and-stile router bit sets about for single-side doors such as cabinet doors. Bit sets to do double sided doors are very expensive, so I wanted to know if anyone has used the single-side sets (made for 3/4" thick) and flipped the 1-3/8 stock to make a double sided door.

single sided

double sided

I haven't, but can't imagine needing a double sided one unless you make doors for a living.

Wouldn't try making this type of door without a very good large woodworking shop. Mating frame and stiles is very difficult. Many of the 2 panel doors used pine or fir plywood for the panels. There are quite a few on EBay. Check "Architechtural resales". We have quite a few in the Atlanta area and they are a good source for period doors.