Dear Jeremy,
Probably, switch of entire CAD runtime is not required.
I checked that the minimal .NET 6 add-in (see attachment) works on SolidWorks 2021. They use COM technologies, similar as it was e.g. for Inventor till 2011, before the way through .addin file was introduced.
I tried the minimal .NET 6 add-in (see attachment) in Inventor 2022 through .addin file way - it displays in the add-ins list but does not load unfortunately. Also, I tried the COM way - registered add-in with regsvr32.exe and setup proper registry entries to get add-in visible for Inventor (as described here, search for ' #Region "COM Registration" '), but it even not appears in the add-ins list, so seems this old way no more supported.
Maybe, if turn on back the old add-in registration way, then Inventor will can load .NET 6 add-ins as it can SolidWorks do for now.
Unfortunately, for Revit it might means to move on COM API to support such thing.
Maybe, if it might be easier and more quick to implement ability to register a .NET 6 add-in via the old way through COM + registry entries, then it would a working solution for nearest years till Revit and Inventor will switch their runtime to .NET <latest>?