How to export web NCBI tBLASTn results in table format with many queries?
It sounds like your easiest option is to just install blast on your local machine and set up the databases there. It really will only take a few minutes to blast 6,000 sentences against a yeast genome on a modern laptop. Any solution interfacing with web results or parsing the output will be painfully convoluted. There are executables for blast that will work on Mac, Linux, or Windows.

Some beginning instructions for installing it on your laptop can be found here: https://blast.ncbi.nlm.nih.gov/Blast.cgi?CMD=Web&amp;PAGE_TYPE=BlastDocs&amp;DOC_TYPE=Download . Make sure to pass the --num_threads option to speed up the search.