I would use MWC instead of LCG generators.
I've been thinking about your suggestion while looking at the MWC algorithm. I'm puzzled about why you think its better for cryptography.
It reveals more of its internal state in the output. The internal state does not have many variables. [EDIT] And the values that the variables are given is restricted to safe primes.
These things make it easier to brute-force.
I have 18 variables, which can take any odd number value, all of which take different values every time an encryption is performed; and these values will likely never be used more than once.
One advantage of MWC is that it is significantly faster. Another disadvantage of my algorithm might be that other algorithms probably take up less storage that 18 * 4 bytes.
I developed my idea as an experiment, and although I think it is fairly strong, I didn't expect anyone else to agree with me.