I wanted to provide a better answer because a) I had some free time and b) I realized its two years after the original post, haha. I checked liquipedia to see if I could find some battle cruiser builds or info and I really couldn't. I played some online games and tried to rush battlecruiser (keep in mind I am a low gold ZERG player) and I found that Battlecruisers are useful if you get them in TvT against some lowlevel players. They're really good if you rush them out (get a trio before the 10 minute mark) if they're going bio. Its kind of a cheese strategy that will work perfectly fine if they don't scout your tech. If you've ever heard of totalbiscuit he has a series for low level players and there is an episode where he actually sort of deals with battlecruisers.I Suck at Starcraft 2 - Episode 20 - Who called in the fleet?
To improve on his design a little, I did two proxy bunker barracks with the barracks much further from his base. Barracks with techlabs can give you some pressure. You can use a number of units from this or lift to make reactors. I don't make reactors, I make a few reapers for harassment. I add starports at that place and lift my barracks to change over the tech labs. I can transition into bansees here, if the build goes too terribly wrong. But the proxyied fusion core allows for litterally no scouting. I try to pump marines and two base early because the early bunker near thheir base allows me to have a massive economic advantage while they switch tech to siege tanks or stems - which isn't effective against my strategy as a whole.
The key is to make sure you have a barracks and an armory in your base so that he isn't able to scout air at all but thinks you're teching for bio or armoured. Remember yamato cannons basically one shot turrets and vikings.