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I think you should not be affected by the SEO of the page, nor should you be penalized by Google. Google penalizes when there are many hidden links to other pages. It is considered a bad practice. For example, years ago, people hid keywords with the background color of the web (penalized by google severely), this is detected by the different changes of the google search engine. I hope I have helped you

Ryan, the Google Analytics tracking code is not implemented in a PDF, it's only actually implemented (the JavaScript code) by the user's browser. So, you're exactly correct: Google Analytics is only showing how many times the PDF link was clicked on from a webpage, whereas GWT is showing all of the clicks when the PDF showed up in SERPs.

Hi Ryan, That's a difficult situation! Usually, what I've found in this situation is that you have to spend an hour or two backtracking to discover where the name of one business is being conflated with the address/phone/website of the other. This might exist on the company's website or website, or it might exist in citations, or elsewhere. In many cases, this type of conflation is what has caused the confusion on Google's part. It's really important when you have a franchise that you've done everything you possibly can to differentiate the various branches, including different addresses, phone numbers, landing page URLs or websites, content, citations, etc. Even then, Google can sometimes become confused about this scenario and begin merging down details. So, if you can backtrack to a source for this confusion and correct it, that may resolve the issue. You can also try to contact Google directly about this (go here and click the contact us button https://support.google.com/business/?hl=en&rd=1#topic=4539639) but you may very well get the answer, "That result is generate algorithmically and we can't do anything about it." Might be worth a try anyway.

Third vote for using the site and not redirecting it here (pending a re-brand of sorts to suit the fact that it's now owned by your company). You have the opportunity to take up a lot more real estate in the SERPs than you do now, whereas redirection at worst removes the old site from the results. At best, you might see a small improvement in your rankings, but you're already ranking better than that site to begin with. As EGOL says, PageRank is logarithmic so if you're dealing with what is a weaker website (whether in actual PR or toolbar PR - the latter of which is a fairly outdated metric but still gets used for basic comparison purposes), it may actually be many times weaker than your stronger domain. At best, using both site might allow you to target different sections of the same audience, appeal to different needs from the audience base (very large clients versus smaller businesses, etc.), and for results where you rank top 10 with both sites, you're about 20% of the results, not 10%

What works for my clients when I help them transition is to do all that's been suggested so far (even considering splitting out the work into phases if at all possible).  But also, it's doing a press release right away, getting social buzz about the new site, and working on adding / building up the content around the core phrases, then link to that new content from the home page. Then focus on link building efforts to reinforce the new URLs.  And see if you can get any existing link sources to change the URLs in those to the new version links - sending much stronger signals than just 301 redirected links. If you do the work properly, you should eventually have both the home page and the inner pages show up for your most important phrases.