Well that's too bad. First off I find that very odd he would keep the old site live. I would yank that immediately after I 301'd my link profiles. If you have ANY incoming links that you find relevant or worthwhile you need to have those redirected to the appropriate pages on your new site. Yoast can do that.
Drop that subdomain. The Way-back machine is always there if you need to reference it, but also you should have it backed up locally just in case.
The sitemap isn't a huge issue, Google will crawl your site assuming there are a few links incoming. As for why your SERPs dropped, that could be due to any number of things. You've got some decent links coming in, but of course we could all use more so get to content building and promoting for sure.
You might want to look at what your old sites did differently in terms of keyword placement. Titles, Headers, Ratio, etc are all important. Just keep in mind it needs to stay natural while clearly being about your targeted keyword. This should be easy enough to do. If I'm writing about bankruptcy that word is going to pop up organically plenty of times. Just make sure it's in your URLs, H1s, Titles, etc. The Moz on-page reports can help with this.
This is all I got right now.. Hope it's at least a tiny help.