I have a similar issue as the OP for a long used project which recently started throwing this error:
"Project '~/filepath/filename.Rproj' could not be opened: file line number 1 is invalid"
I was able to open the .Rproj file with Notepad ++ and it showed a single line (218 characters) of all 'NUL' (Ascii code 0 from what I can gather from the internet). Looking at other .Rproj files, the 'NUL' is different and, I assume, not good.
Looking at other .Rproj files, generally they all seem to have the same information on my machine:
With slight variation if its was related to a R package.
I was able to copy and paste the text from another .Rproj file into the corrupt .Rproj file and the project will open now.
Hopefully this will generally help.