I totally appreciate the requirement for excellent, one-of-a-kind cover letters. I'm also advised to send out a slew of applications. I haven't been able to balance the two. How are we going to deal with that?

It is never a good idea to prioritize quantity over quality in your job hunt. You won’t be able to explain to any of those employers why you’re the ideal match for their firm or that specific position if you send out a slew of applications. That is exactly what employers want to see.

Rather than sending out a large number of applications that are not suited to each job and company, send out fewer applications that are more specialized and more particular to each job and firm, including tailoring the CV and cover letter. You may not have as many applications, but they will be more intriguing and well accepted by employers.