I got the sanitized return from support agent. I see you selected to e-file federal return, that's what triggers the error "Partnership Information Worksheet: Today's date must be entered for electronic filing" on federal information worksheet Part VI, Date PIN entered field. You mentioned you entered the signature date on LA information worksheet. However, there is no signature date there. I think you might have entered a date in Part VI, Electronic Filing section for "Date return was electronically filed". You don't need to enter that date for extension filing. 

The root cause is because you selected to e-file federal return, Fed information worksheet Part VI, Date PIN entered must be entered. 

Sorry for all the churns you ran into. If the extension files successfully, you will see a date populated on LA information worksheet, Part VII, Extension filing date field. 

Hope this is helpful. Do let me know if you run into further issues.