In light of the new findings, the data table in the original post now looks more familiar:
It resembles a data table that, in the first step ('V1'), was exported with quotation marks added to the numeric and character columns (just the first column didn't get the additional quotation marks:

Surprisingly:
V1 can be opened in JMP and Excel via drag and drop. Both programs automatically 'unpack' the CSV quotes and load the table in the correct format. So, how do you get from V1 to CSV with wierd sep.csv ?
What works:
step2: open V1 as tab-separated table (instead of a CSV file with CSV quotes)
step3: save the table as csv (in this step [in JMP and Excel], the additional quotation marks at the start and end of each row are added automatically and single quotation marks are replaced by 2x quotation marks)
The reverse process should be straightforward:
- Just open CSV with wierd sep.csv in JMP or Excel. Both programs remove the enclosing quotation marks automatically, and double quotation marks are converted back to single ones: This is how it looks in Excel:

exactly like what we want:

So, let's save the data table as a csv - and load it again : )
in JMP, we can disable the options:
]
Unfortunately, the CSV encoding is enabled by default. On the one hand, it's reasonable — saving the file without CSV quotes would change the data structure significantly!
But actually, that's what we wanted.
So, the only way (?) is to copy the entries from JMP or Excel to a text editor and save v1.txt from there.
The text editor doesn't know about csv quotes and saves the text as it is.