I like my toast like that too, and yes, home-made sourdough can be a bit challenging.
But it can and does make the most excellent toast.
Firstly, it can only be cut into fairly thick slices: that's not to everyone's taste. The middle will only get a Bit Warm when the outside begins to toast.
When it's fresh, you really can't toast it. When put in a toaster, the crumb has too much moisture and doesn't toast. But the crust just burns.
But when it's a couple of days old, it's much more toastable as it has dried out a bit.
I often use it for breakfast things like kejriwal, and find that toasting it on a hot griddle over the hob works much better than a toaster.