Andrew,
It seems that, although it was mostly removed when I performed the removal process, it had broken my TCP/IP stack. At that point, I had performed a system restore to before the point I had removed Web Companion. While this did not entirely restore the program, the DLL was restored, as well as certain registry entries.
Unfortunately, this puts me into a bit of a predicament, as it seems any attempt to remove Web Companion completely will break my TCP/IP stack again. The most I can do is remove it from Add/Remove Programs and the Modern Apps list in Windows 10 (which does not seem to be enough, as the LavasoftTcp64.dll file is still in system32, and I cannot remove it since it is still in use by dasHost.exe).
Further, a system reset won’t help, as the program was likely installed because I have an Acer laptop and therefore Windows gave me what would’ve been installed on an Acer OEM Windows 10 PC.