Seems like you should focusing on optimize this revenue stream. 

The optimal opportunity would be to do an FHA 203k loan on a 4 family and refinance.

Weekends are higher than weekdays, busy season is higher than slow season, holidays and special events are higher than regular days… if your goal is to have some degree of optimization you need a thorough understanding of your market that even a dynamic pricing tool doesn’t provide.

Survey: Small biz owners excited about the futureBusiness owners' optimism about the U.S. economy and the outlook for their own businesses has reached levels never-before seen in the 15-year history of the PNC Economic Outlook, a biannual telephone survey of small- and medium-sized business owners.A strong majority of small business owners (88 percent) surveyed are optimistic about the near-term outlook for the national economy, up from 71 percent in the fall and 56 percent last spring.

(Brother the plumber, sister the electrician etc etc)5) Train chimpanzees for the labor because you do not require workers comp insurance on non humans.EASY AS 1 2 3 This is the best way to optimize your profits in building

In addition, Danny, who is a computer geek of some sort (Sorry Danny, but I do love your story about what drove you from geek-world to flipping) uses his flipping experience to optimize a website for what we all do.....wholesaling, flipping, getting leads...the website is so user friendly it allows you to tailor whatever you want to focus on,wholesaling,  RE selling,,,,and it comes crystal clear videos narrated by you guessed it Danny the ace flipper ;)If BP was amazon, i'd give it 5 stars.Nice addition to BP.

*Why* is it so horrible that the gross annual rents come out to a quarter of my optimal buying price? 

Perhaps a portfolio minimum average rent.Create a marketing plan.Learn search engine optimization so your company can be found easily on Google.

My first property was in a less-than-optimal area and, although in Japan, this isn't nearly as bad as it is in the USA, it was still a lot of pains for a first deal and a steep learning curve.I'd advise against it, even if it means waiting a bit longer for the right deal to turn up in anywhere that's even slightly better than what you're describing - basically a mini-warzone, from the sounds of it...

Do you think there is an optimal sequence for upgrading your rental property?