Well, David you were correct about the ID and that led to a solution today. Finally.
I've been an Apple user since 1986 and I believe I had an ID well before the App Store appeared in 2008 and certainly before they assigned the icloud email address as an ID. Today my wife found the old 2013 bank book that had the purchase noted in it. I didn't need it though. I found an old note to myself with the user name I used when I purchased Logic. The tricky part was that my old account did not use my old password but the new one. I had to trash my current Logic program and was able to download from my old account. It asked if I wanted an older version when I installed from the App Store, but I am up to 10.7.9, the latest Monterey can use. I think the latest is 10.8.1, so I'm not far behind.
More than two hours on the phone with Japanese Apple support. Their number for English didn't work. Kudos to my poor wife who is exhausted after translating and talking about stuff she doesn't understand for more than 2 hours.
I asked if I could combine my oldApp Store account with the new one and they said no.
Thanks to all for your input.
PS I got another computer. It is exactly the same model early 2008 MacPro, but with more RAM, a much better graphic card and a different USB3 card.