Has there been any research on entropy efficient information-theoretically secure PRNGs?
Since you are looking for an algorithm that guarantees entropy for the output if the input it entropic, you are not actually looking for a PRNG, which would expand a seed to a longer random output, but only a transformation from a binary sequence to arbitrary values.

You can achieve this using arithmetic coding, or range encoding, which is the same thing in a slightly different manner. It is a way to encode values from arbitrary probability distributions into minimal size. In your case you can decode a random "seed" sequence to extract random values in any interval(s).



Caution: normally it is fine to be slightly inexact in the encoder math as long as everything is deterministic, since that only worsens the encoding rate slightly. In your case, for secure random numbers the possible outputs must be equally probable so typical implementations may not work for you. Rounding must be done in a way that ensures this.