Ok, with much struggle I've finally answered my own question about how to run a background dos program in a minimized window. So I thought I should share it. My solution is to follow the background dos program call with another dos program that minimizes the first window as follows:
WinMin.exe is a program I created myself. If you would like this exe, you can make it by creating a text file with the name WinMin.ahk that contains the following single line:
Then install "autohotkey". Then right click on the ahk file and select "compile". That's it ... you'll have your very own dos window minimizer. And by the way, the call to WinMin.exe does not create its own dos window because it does not need to run in the background and thus does not include the trailing ampersand character.
I was thinking of putting WinMin.exe on the file exchange, but I would feel a bit silly doing so since I suspect there is a simpler more elegant method routinely used to do this that I just don't know about.