I haven't tried it myself yet, but you can get yeast improvers , a powdered 'mother yeast' that claims similar results to sourdough.
I have a starter in the fridge that I only use once every two or three weeks, and have not had any mould problems; perhaps you just have to be only a little less lazy to keep a viable one, and feed on that sort of a schedule?
I agree though, that making sourdough bread can be a nuisance time-management-wise until you find some sort of rhythm that suits you.
Apart from the hole, that could be chicken on a raft, an old Royal Navy dish.