Hello, DJHorton!
Perhaps I can assist you, given that I'm an online dating veteran. Much like you, I have tried to increase my efficacy and have found out several things.
The first of which is the fact that the big reason that you're getting this message "black hole" effect is due to how the site is designed. On OkCupid, the user interface works in a fairly symmetrical basis. You can message people at any point and don't need to see likes to do it. In fact, unless you're an A-lister, you'll have no idea who likes you. You just know that someone does. So, most people skip to messaging directly.
If you are a woman on OkCupid, instead of a black hole effect you'll become swarmed with messages and likes. I know this because I have several female friends on the site and it's pretty evident from a cursory glance. This means that you'll have to be very selective about who you respond to because you definitely can't respond to all of them. Some messages that would normally warrant some sort of response inevitably get lost in the mix because there's just too much.
Newer dating apps and services offer a different model. I don't particularly like Tinder and wouldn't suggest it for a serious relationship since it seems more geared towards hookups, but it does one thing right. In order to facilitate communication, both parties must match with each other. This means that there's less stuff in your inbox when communication does happen.
Fortunately, there are more relationship-oriented services that use this model. Coffee Meets Bagel is one of them. You only get one match per day, but that means that you have a better chance of success than if you were one in a sea of hundreds. The only downside to that service is that you can't select for interests, which is a really important factor to me. There is an app/site called Dragonfruit which is particularly suited for geeks like myself, but the app needs more QA (I honestly can't believe they released it in its current state) and I'll probably just end up using the site in the meantime.
I'd also like to note that Coffee Meets Bagel actually has some really good dating tips, which I wish I knew earlier. It includes things like gauging interest from text messages, when to advance in relationship stages, and so on. I wouldn't take their advice as literal 100% absolute dictums, but they're helpful guidelines.
So, to summarize, go for a site/app that does a "curation" model that requires the parties to match before communication can begin. Unless your profile is the absolute best, you're going to be fighting an uphill battle otherwise.