Does anyone know an easily creatable asymmetric cryptosystem for usage in VDF?
The issue of having to factor a large number in ElGamal appears only if you set the group order to be an arbitrary prime $p$. In this case, to find all subgroups of $\mathbb{G}$, you need the factorization of $p-1$.

However, this issue entirely disappears if you take $p$ to be a safe prime, i.e., a prime number of the form $p = 2q+1$, where $q$ is also a prime. Finding such primes is not so hard, and testing primality does not require to compute any expensive factorization.

Once you have $p$, sets $\mathbb{G}$ to be the sugroup of quadratic residues (i.e., squares modulo $p$) of order $q$ in the field of order $p$. Note that every quadratic residue (except $1$, of course) generates the full group of quadratic residues, and testing whether a number is a quadratic residue can be done efficiently. Therefore, there is no possibility that some ElGamal key in this group is invalid: any quadratic residue $h$ not equal to 1 is uniquely associated to a secret ElGamal key $s$, which is the unique $s$ such that $g^s = h$ ($g$ is some fixed generator of the group). Even though brute force to find the key is not efficient (that's the whole point of it, in fact), it is guaranteed to succeed (in exponential time) in finding the unique ElGamal key.

Therefore, it seems to me that a properly instantiated ElGamal scheme should suit all your needs.