Hi Shania,
You really think this that they are very old, having most of links from paid. Follow my advice to do the whole process what i said. You can't say you don't have places to work, as I compared and saw the differences you and your competitors have, to look at here. You still need to gain your domain and page level authority than your competitors, it can only be possible to do gaining the link vote which you could get the way I told. I am pretty sure If you take all these four competitors in your competition box to extract all their external , there are still a lot of places which you can approach to build links, yup it takes time to be done all. But it must help you to get compete your competitors pretty well and cross them to bring you to the TOP as you want. that's it!
Regards,
Teginder