Has anyone tried to re-install a downloaded copy of TT onto another of your computers after the original computer "died"? I get a 607 Error Code.

For what year?  You should be able to install 2020-2023 on another computer.  Are you trying to download the program from your online account or from what?  Sorry I don't know what  error 607 is.  If you are trying to install 2019 you can't.  And if you install older than 2020 you won't be able to update it or download any state programs you might need.  They only support the last 3 years.  

Just found this article,  Reinstall Turbo Tax for Windows 8.1/10/11
https://ttlc.intuit.com/turbotax-support/en-us/help-article/reinstall-products/reinstall-turbotax-windows-8-1-10-11/L9Ogh72oN_US_en_US?uid=lviebvx4