Some great suggestions by Adomas. Here are few more you can try -

- target people who like brands (which you sell on your site)
- target people who like 5-10 competitor's sites (for each product category)
- find pages/interests liked by people who like your page and get ideas from there
- expand your lookalike audience beyond top 1%

Above should help you expand your reach. Now to increase conversions, you must do re-targeting for those who visit the site and you must keep expanding the lookalike audience based on your "buyers" list.

If you need more help in setting up or scaling up huge campaigns, let me know.

If the content is of high quality, there can be only 2 possible reasons on high level - #1. duplicate content or multiple thin pages within site and #2. Bad link profile. As you have pointed out, there are other sites republishing your content - but that's not termed as duplication (it's a case of syndication, which is perfectly normal). There are few things you should take care of while doing syndication - like using nofollow backlinks, referring to source etc. I have been helping clients successfully recover their sites for quiet a long time now and have never seen syndication as an issue. So if you want me to take a look, feel free to schedule a call and I'll take a look.

Break it in 3 phases - 1 month, 6 month & 12 months. Tell them what you'll "do" in 1 month and then tell them what they'll "get in results" after 6/12 months. Map results to their revenue/traffic.

Now give them an irresistible offer - if they extend the contract to 12 months within 30 days of signing up , they get X,Y,Z extra worth $XXX. These free things can be landing page's conversion optimization, paid media buys every month, monthly press release for media exposure etc. Think what else might help them as business an club those in free package.

Adwords is not the best platform when you want to target an "audience" instead of search terms. I would suggest you to use Facebook - targeting lawyers - or may be display ads - targeting pages visited by lawyers - and call out your app details in the ad copy. This will make sure that the persons clicking on the ad are from your target audience and are interested in what you have to offer.

There are some great suggestions here if you want to learn things on your own. But if you want to just focus on client acquisition or want to keep it lean/simple initially - just find a good partner/reseller who provides SEM services. It's better to spend money paying for SEM services if that's not your core strength and play with your strengths in other parts of business.

Topic targeting is a broad way of targeting people who've expressed interest in that topic or "related topic". It's a good option if you want to create awareness, do branding or generate likes. But when your end goal is sales/leads - it's good to go for precise interests as that's like exact match - and it ensures that you're reaching only those people which you're actually targeting - not related ones.