Can you use a too runny cake batter for anything if it can't be used for cake?

Add some baking powder and cook on your waffle maker!

Add the leavening, crank up the deep fryer & make chocolate beignets, or some kind of funnel cake/etc. You may have a soufflé base as well. Maybe roulade?

Oh, this is interesting! Sailors have a great expression: when you don't know what knot to tie, tie lots of them. I'd probably do this: I'd add ground flaxseed, say, 2 tablespoons per cup of batter, and a beaten egg (which will firm up once cooked, helping with the structure of the baked good) per two cups of batter. I'd bake it on a large sheet pan, not very thick, i.e., an inch or two of batter. I'd bake one tray and then see what happens. If it comes out okay, I'd use that thin layer in a layered dessert, e.g., something like a rustic trifle, or I'd cut it to the size of a loaf pan and layer it with ice cream, starting and ending with ice cream. Line the loaf pan with parchment in a sling. Freeze until super hard. Soften some ice cream by beating with a sturdy spoon (don't melt it any more than necessary) and swiftly "frost" the cake with it right away. Pop it back into the freezer. Slice and serve no less than 3-4 hours later. You could also break up the baked end result, dry it in a low oven for 20 - 30 minutes, and use it for rum/bourbon balls.
I can't wait to hear what others here suggest. And to hear what you end up doing! ;o)