Do Southern Chinese speakers have any greater propensity towards using 啦 than Northern Chinese speakers?
So do southerners actually say 啦 with any greater frequency?


Yes. Cantonese people and their excessive usage of 啦 is already a widely known stereotype.


  I've never heard Singaporean Mandarin, but does that include a lot of 啦? 


The standard dialect used in news broadcasters are quite similar to Mandarin in China. 啦' s usage in daily speech may vary, depending on your background.


  Is this a real thing where southerners take something that sounds equivalent in their native dialects and sprinkle it into their 普通话 or am I an odd one?


It's a real thing. Not just southerners, everyone in the world has a natural tendency to do so.


  Is it viable for me to add 啦 to the end of many sentences?


Excessive usage of 啦 in Mandarin is like excessive usage of "You know" in, you know, English, It's, you know, kinda annoying. While I applaud the usage of dialectical phrases in Mandarin, using 啦 excessively is only an indication that your Mandarin needs improvement.


  Would I sound extremely strange to say things like “我们去吃饭啦” or “你说啦”？


Not really strange because most people know too well how a southerner would speak. Still, it's better to use "我们去吃饭了", "我们去吃饭吧", and "你说呢".