[Arran]

I rarely find a reason to disagree with Arran, but in this case I have to. The woods listed (maple, birch, or beech) are not normally used for trim or case work. They are difficult to finish, especially Maple, and they are not known for being dimensionally stable.  Two woods that are easily obtained and that are both free of figure and physically stable are Poplar and Basswood. Pine is also a decent choice provided that it is clear grain (free of knots).

John;
  I did state that I believed that Tulip Poplar or Gum wood were likely what they used for the trim originally. However these trim pieces look like flat strips so you could probably use whatever tight grained wood you could find and it would work satisfactorily. Tulip Poplar was often used for moldings because it's a relatively hard species of poplar, it's relatively free of defects, and it's easy to machine. I have seen maple, and or, birch or beech used in radio cabinets and other furniture, and I have also seen ash used for the same.
 They also often mixed and matched different species in the same cabinet, such as using veneered maple in the top, and poplar in the millwork, and Fir plywood for the chassis shelf, I have a C.G.E JK-76 cabinet that was made this way. I have had a few Rogers/Majestic/Deforest cabinets where the cabinet company used ash for the sides, cabinet bottom, chassis shelf, and used poplar for the millwork, I think that they used whatever was inexpensive yet still suitable for the job, maybe MacLaggan or Kneichel could get ash for a cheaper price then they could poplar or maple?
Regards
Arran