The most explicit path for you is to access this with multiple reads, i.e. get the main data rectangle (specifying the range) and either use another read (or two) for the tricky column headers or just apply column names "by hand".
You could use readxl for the above or googlesheets (both on CRAN) or googlesheets4 (only on GitHub right now).
Alternatively, if you've got local xlsx, you should check out tidyxl (on CRAN) which is specialized in this sort of tricky sheet.