Just can't get this to budge!!

So I'm helping someone try and push a government PDF link down in the search engines. It's a state supreme court file.
83 DA, 76 PA (Homepage)
534 Root Domains
3,312 Total Links

This page simply wont budget. I've been working on rankings, Twitter, Facebook, Linkedin, Yelp and many other pages to push it down, but all that seems to be happening is they bounce around it. If one goes up, another drops below.

I've created a total of 1350 T2 and 900 Tier 3 links to about 10 different pages and profiles.

Should I just bout some fiver gigs to blast the hell out of some of these things and wait?

I'm getting really frustrated. Any advice would be great.

A .gov site, with over 500 root domains? And probably many of those root domains are powerful (other .gov sites, news site, etc). It sounds like a web page that legitimately belongs at the top of the serps. Does it seem right that shoveling spammy links at social media account pages should move those pages ahead of the .gov page? It seems to me that in this case Google's algorithm is probably getting things right.

Might be true, I've pushed some of the pages above it, but then others there were above drop below it. If I stop the links and wait and watch, all the positions on the first page dance a bit and resettle pretty much where they were.

It depends, what is the court file about?

Its a case report that didnt amount to anything. Someone took my friend to court (his business) but didnt follow through or something, but now the pdf report is in google in the middle of everything else he has ranked.

Don't blast it, it won't do anything, especially with latest Google update and the strength of the domain. I tried blasting a much much weaker domain with 100k backlinks and it did nothing.

Op if you cant do it just hire somebody else (Outsource), you need expert to push gov site to 2nd page.

Ok, you can try to contact the owner of website and explaining the situation and asking him to remove the pdf from the website, in case it doesnt work try to offer to pay for him to remove the pdf from the website

Yeah, I was going to call tomorrow and see if it was possible to have them remove the case file.
Basically, the only way I assume to push this down in the rankings is to measure all of the backlinks authority linking to the gov site and then try to match the same power in links to the surrounding sites.
Thats going to be very expensive.