You will be able to upload using Logicmaster even if the program was originally created with a handheld. I have several sets of Logicmaster installation floppies dating back to the nineties.
Changes made in 2003/2004 could have been made with VersaPro. If that is the case, you won't be able to upload with Logicmaster. However, given your problems uploading using Machine Edition, I think the odds favor a Logicmaster program.