1. Actually 17 is not horrible depending on what this person is doing. Is he searching for opportunities, checking links and then contacting the webmasters with fully personalised emails? If yes, then 17 is OK-ish. It's just 28 minutes per site.
2. Hire more people :) Ok, on a more serious note, depends on how much you want to spend. You can streamline the process by giving it a bit more structure. For example:
- Use advanced search queries to find resource pages within your industry
- Use Xenu Link Sleuth (free tool) to identify the broken links
- Branch out by finding other sites that link to those broken links that you just found
The last point is the most important. It's pretty exciting - you start your day with one BLB opportunity and end it with hundreds. If you've got money to spend, you can subscribe to MajesticSEO and use it for "branching out."
Let's say you find that Site A links to Site B but Site B is dead. Now enter Site B's domain into Majestic and see who else links to Site B. You can find dozens or even hundreds of BLB opportunities.
Or if you don't want to spend money on MajesticSEO, you can use advanced search queries to find who else links to Site B. Something like: resources "Site B's Title"
or "Site B's Title" inurl:links.html
I will say, however, that you are doing the right thing, and the only way BLB will ever be successful is when you do it manually. A "lot faster" is likely to disappoint you.
Just out of interest, what success rate are you getting with the current approach? So, he's getting through 85 opportunities per week. How many of them will bother to respond and how many will give a link?