So sorry you're going through this frustrating mess! I'm sure you paid into having the benefit of STD/LTD so it's not like it welfare! Did you go through the FMLA process through HR.....STD etc.?
I'm going through something similar but thankfully I got my STD and it transitioned into LTD but they hound me every week or two to check on my application process (they require) for S.S.D. It's still only a fraction of my regular pay but It helps.
Depending on how much money you could get the $4000 up front atty. may be well worth it in the end.
It's hard for me to write long replies because my RSD/CRPS is in my hand and I can only use one finger for a short time on that side. So sorry for lack of more details right now.