Instead, you might look at techniques like Burmester's theory to design the proper kinematic linkage between them. You could think of an Ackermann system as two bicycles welded together side by side, noting that connecting the front wheels is not solved by simply forcing their steering angles to be equal. In other words, you end up with a "steerable front beam axle" like you'd find on a toy wagon - not an Ackermann system: At first, the tire gets wider, then splits into two tires, then they get further apart - but the axles of the two wheels remain on the same line.
Rather than thinking of Ackermann steering as (conceptually) a single wheel, imagine expanding the single front wheel of a tricycle into 2 wheels. You're making two mistakes that I can see, both related to the idea of "shrinking" the set of front or back wheels into a single wheel.
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