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Dear Tony,
Thanks for your updates.
Sorry for that I may ignore the Retail version of Viso in your environment.
I think that the root cause is that the Visio 2021 is retail not volume license and Office 2021 is volume license not retail. Based on the message "Products installed on the same computer must use the same update channel. For example, the volume licensed version of Office Professional Plus 2019 can only use the PerpetualVL2019 update channel.", you need a Visio volume license in your environment.
The best next action is to install Microsoft 365 applications and Visio 365 application directly as you mention that you have Viso 365, Visio 2021 Retail, Microsoft 365 applications and Office 2021 LTSC.
However, from the description "We can't upgrade to our licensed O365 suite until February after our current on-premise document management system is migrated to the cloud (iManage cloud).", it seems that you can't install the Office applications. So the next step is to buy the volume license of Visio in your environment.
The example product id "VisioProRetail" I provided in the code is for Visio 365 not Visio 2021 Retail. Given the situation, you need to use VisioPro2021Volume and use the code like the following.
<Configuration>
<Add OfficeClientEdition="32" Channel="PerpetualVL2021">
<Product ID="ProPlus2021Volume">
<Language ID="en-us"/>
<ExcludeApp ID="Lync"/>
</Product>
<Product ID="VisioPro2021Volume">
<Language ID="en-us"/>
<ExcludeApp ID="Lync"/>
</Product>
</Add>
<Property Name="SharedComputerLicensing" Value="0"/>
<Property Name="FORCEAPPSHUTDOWN" Value="FALSE"/>
<Property Name="DeviceBasedLicensing" Value="0"/>
<Property Name="SCLCacheOverride" Value="0"/>
<Property Name="AUTOACTIVATE" Value="1"/>
<Updates Enabled="TRUE"/>
</Configuration>
You can use a VM to install the volume license of Visio to see whether it can be installed together with Office 2021.
If yes, you may contact the Visio provider to see if you can cancel the application and buy a volume license of Visio.
Your understanding is highly appreciated.
Welcome to share any updates if you need further help on this issue.
Thank you for your effort and time.
Sincerely
Cliff | Microsoft Community Moderator