I have ranked many easy keywords only building expired Tumblr and expired Weebly, there is a lot of crap out there, but there also very good expired web 2.0. I would suggest you to buy scrapebox, some proxies, and a VPN. For under $100, you can get a lot of expired web 2.0 and you can rank easy keywords. I have expired Tumblr that have links from nymag.com, mashable.com, elle.com, cosmopolitan.com, harvard.edu, and so on. You need to filter them manually, I suggest you to set a minimum trust flow of 4 for analyzing them. If you build many of them you can even rank a medium competition keyword, but it depends.
Some universities, some companies, and some rather famous people have their own tumblr and weebly. Finding a web 2.0 with edu links is not that difficult