Quote:
DURING the World War Ex-President Theodore Roosevelt suggested that a
series of stamps be issued to commemorate the American Army and Navy
heroes. From time to time other organizations suggested special series
of stamps, but no definite action was taken.
On March 6, 1936 the series was announce but without details.
The actual persons and designs selected for the series were not announce until May 5, 1936.
After the election, on November 23, 1936 it was announce that the designs were created and announced in text with illustrations via photographs of the official drawings. These drawing were used as models for then engraving the final stamps. The final engraving used various paintings or statues as the designs guiding the engravers of the actual stamp dies.
The above information quoted or gleaned from The United States Postage Stamps of the Twentieth Century, Volume 4 Commemorates 1933-1937 by Max G. Johl (a great uncle)
Given the fact the series of stamps had been kicking around almost 20 year, the sheet in the OP could have been an attempt to influence the series creation (as far as the navy portion). After the series were announce, without design details, the examples shown in the OP could have been created to influence the selected individuals as well as used as the basis for the original drawing and as such the quality of the engraving did not matter.
Lastly it could have been created after the drawing were announced and shown. However, the suggestion that they were to be cut out and affixed as cachets for the various first days falls flat as such are not found on FDCs as far as I am aware.
Edited to correct flawed text copied/pasted in quote.