Is there any existing cipher capable of scaling from a 1 bit key up to a one-time-pad? We have ciphers that handle small amounts of entropy, such as a 256 bit key for AES; and we have one time pads for enciphering 1:1 entropy, such as a 1GB key for a 1GB file if you could ever harvest enough decent random noise. 

Now in theory you would imagine that there is a universal class or model of cipher that can scale smoothly from a single bit of entropy all the way upto a 1:1 one time pad.

If such an algorithm or cipher already exists - what is it called?
a one time pad ia very different from other fixed key ciphers.
A one time pad is just a xor(or modular addition) It does not miz anything or extend key and even a tiny bit of key reuse is very problematic.
We have stream ciphers which take a key and produce an infinite stream of pseudo random bits.
Perhaps what you are asking for is for a cipher with arbitrary key size with guranteed perfect security for total message length less than key size and reasonable security for reasonable key sizes.
I can suggest the following construct. take the key and duplicate it by concatenation to produce naive infinite key.
Use Each key block to encrypt a counter like in CTR mode.
This by itself doesn't give perfect secrecy. You could then xor each block with the following key block. That would give  perfect secrecy when message is at least one block less than key. It might be possible to do better. But this construct will give at least the security AES CTR.