Wow!
So after over two hours of trying to figure out what's going on - during which I must have uninstalled and then reinstalled every single permutation of Visual C++, both x86 and x64, from the 2005 versions all the way to the new 2022 redistributables - I finally got the launcher to work.
Bizarrely and counter-intuitively, the solution was to go to an unofficial DLL downloading site (which I saw several posters on the Microsoft forums and Reddit recommend against), download the *32-bit* versions of MSVCP100.DLL and MSVCR100.DLL, and place these
32-bit DLLs in Windows 10's
64-bit DLL folder at C:\Windows\SysWOW64. At first I tried downloading the 64-bit versions of these DLLs and putting them in SysWoW64 - because that actually makes sense - but to no avail. But the 32-bit DLLs, placed in SysWoW64, finally allowed the launcher to start up and I'm now finally able to open the launcher to download the game.
( Links to the download pages -
https://www.dll-files.com/msvcp100.dll.html and
https://www.dll-files.com/msvcr100.dll.html )
Hope this helps anyone who runs into this issue in the future. I've seen more than a few posts around the internet from folks who had this problem, never found a solution, and apparently have not played LotRO since.