I see ..., that's not an awk issue, but an OS one. I doubt though that the limit of files in one dir is only 10, it's got to be way more than that.
I tested the codes in Solaris, and they bombed out only after ~ 55000 files were created in one dir, they were all in good shape,and my test file had ~1,500,000 lines.

Well in this case I'd suggest to split the file in smaller chunks ( see man split pages of your OS ) to the size that the codes would not fail, create the same number of directories as the number of chunks created, move these chunks to the newly created dirs, and run the given codes separately in each of these directories created.

BTW if you're on Solaris use nawk.