I've seen some POW ideas that I find intriguing for other reasons like amiller's idea of using fast random access to the txout set as proof of ability to rapidly process Bitcoin transactions but I've not seen anything that prevents people with custom hardware from getting a substantial advantage over the public except by getting specialized hardware into the hands of the public.
I second that. We'd need more ideas of how to implement a fair POW system which cannot be easily corrupted. Satoshi ruled against Proof-of-IP, because it's even easier to attack.
A fundamentally fair system rewards the miner by their contribution to the network (in terms of transaction processing and related services). The difficulty increase does not add any beneficial factors to the bitcoin network, except resilience against a 51% attack. Thus the focus should lie on how to implement resilience against 51% attacks without the consumption of a lot of energy.