Nor am I, but I don't think that's the problem. It seems to me is that if you want to do that, you would use the value as a seed to set the internal state of t

Nor am I, but I don't think that's the problem. It seems to me is that if you want to do that, you would use the value as a seed to set the internal state of the PRNG and then call the PRNG just once to get the hash value. But in order to do that, you would have to derive the seed from the data in an appropriate way, which is basically the same exercise as defining a general hash function (i.e. projecting a data of arbitrary length into a set of values of fixed length). So it looks like you are back to square one, more or less.