Short Term Disability Advice- UPDATE

Jaclyn
Update at the bottom!!! Seeking advice from anyone who has had to use Short Term Disability for maternity leave. Is there anything that can be done to be granted more time off? Anything I should know about when I file my claim. Any advice or notes on your experience are appreciated. I don't like the idea of flying blind into an insurance claim situation.  I've been quoted 5-7 weeks for vaginal and 9-13 for csection delivery- side note, is it not crazy that in the US a woman might ever have to have the thought of "at least if I have a csection I get to be with my baby longer!" NUTS! (Also, I'm a govt contract employee and was forced to change companies in April at 6m pregnant. I haven't been employeed for 12m so I don't qualify for FMLA. I'd been with the previous company 3yrs) 
UPDATE:
HR contacted me today to notify me they have approved FMLA for me by honoring my hire date in my position and not with their company! Still working full time until 7-22 but I now am not under pressure to be induced or return to work as soon as STD runs out!!!