LDR with really low minimum resistance for a VACTROL vibrato

[wax+wire]

so i want to build a vibrato into a keyboard.  It has already been clocked with an LTC1799, so i thought putting a vactrol LDR/LED in series with the frequency potentiometer might be a neat solution.

ideal the resistance would oscillate between 0ohms and say 1k ohms .

trouble is, I can't find a LDR that gets down to 0 ohms.  I understand I can put another resistor in parallel with LDR to reduce the resistance of the maximum, but if the LDR never gets to 0, or close, then neither will my overall resistance.

I'm going about this the right way? any tips?