This is not an ODS or Base Reporting procedure issue. The MISSING option in Base SAS works to alter the DISPLAYED value of a missing variable value -- such as when you use PROC PRINT, PROC REPORT, PROC MEANS, PROC FREQ, etc. The MISSING option does NOT change the internally stored value of the missing value -- it is the internally stored value that your information map is using.
Your best bet for help with an Information Map and Web Report Studio question is to work with Tech Support. I believe if you had OPTIONS MISSING=' '; (quote space quote) BEFORE a PROC PRINT, then your displayed results in a stored process would show a blank instead of missing. However, I do not believe your existing code will work as you expect.
Tech Support can gather version and configuration information from you and can test a similar stored process in the same enviroment.