Theoretically, any type of bike--road, mountain, cross, etc., can be "custom." So, I wouldn't say "custom" and "hybrid" are mutually exclusive. As it's generally used, hybrid simply means a bike that had some of the attributes of a mountain or cross bike and some of the attributes of a road bike. It might have wider tires and a suspension fork, for instance, but primarily be intended to be used on pavement.
I suppose in some respects your bike is a hybrid of sorts, but I would be more inclined to define your bike by how it was intended to be used--as a road bike. It might be less perplexing to some, I suppose, if you had narrower tires on it, but who cares what others think? Or tell them it's more or less a cross bike, as that's an apt description, too.
You certainly aren't the only person out there who has a unique set up to serve their precise needs. True bike people (rather than bike snobs) get that. Whether it's steel versus carbon, Campy versus Shimano, compact versus traditional geometry, etc., etc., you're going to find people who want to debate bikes as if one size fits all. There's one "right" thing, and no room for disagreement. I tend to avoid those people. They're not worth the energy.
Live with intention. Walk to the edge. Listen hard. Practice wellness. Play with abandon. Laugh. Choose with no regret. Continue to learn. Appreciate your friends. Do what you love. Live as if this is all there is.
--Mary Anne Radmacher