Thanks to all who have replied! About the vase- it's 13 1/2" high, 8 1/2" diameter at the top, 5" at the bottom. The bottom is finely ground with a round depression in the center as shown in this additional photo. The top edge is formed, not ground. There are several bubbles in the glass...the clear panels were built up in ribbons. The overall glass thickness is ~1/2"- this is a heavy piece. There is a fair amount of wear on the vase, on the bottom, scratches on the sides, and some wear around the top rim. Looks like it was rolled on the floor at least once.
The signature/mark is in the center of the round depression on the bottom. It appears to have been made with a vibratory etcher. It is a single line, starts out faint and goes to practically nothing. It may start with an SS(?). It is so small and faint that my poor camera can't capture it.
I have reason to believe the vase is in fact ca 1940-41 or earlier. It comes from an old estate, and the story of it's purchase was told to me by a woman who was a child at the time.
Thanks again for all of your help!