A 2DES like cipher $c=E^{(2)}_{K_2}(E^{(1)}_{K_1}(p))$ where both halves have an $n$ bit key is vulnerable to a meet-in-the-middle attack.

Meet-in-the-middle using a big table

Create a table containing $E^{(1)}_{K_1}(p)$ for all possible $K_1$ and computing $D^{(2)}_{K_2}(c)$ for all values of $K_2$, looking for a matching result.

This approach requires a big table with about $2^n$ entries.

Meet-in-the-middle using cycle finding

An alternative approach would be to define a hash function that maps an $n+1$ bit value to another $n+1$ value:

Use $1$ bit of the input to decide between $E^{(1)}_{K}(p)$ and $D^{(2)}_{K}(c)$ and the remaining $n$ bits as key for this function.

A collision of this hash function can either have the same discriminator bit, in which case it's useless for our purposes, or different discriminator bits, in which case it's a successful meeting.

Now search for collisions of this hash function, applying the usual memory reduction techniques like cycle-finding and/or distinguished points. This should require only around $2^{n/2}$ table entries instead of $2^{n}$ table entries, while increasing computation cost only my a small constant factor.

Does this approach work?