Asymmetric password encryption - Viable? Which algorithm?
This seems OK assuming you can trust the authentication servers to leak neither the private key nor the deciphered passwords; and, if you use RSA, assuming you use a standard encryption padding with randomization, e.g. one of the two RSAES schemes in PKCS#1.

Elgamal indeed can give you shorter cryptograms, which might be desirable in the context (an Elgamal cryptogram consists of two group elements; thus when the group is a 256-bit elliptic curve, you get security arguably better than 3048-bit RSA for 17% of the size of each asymmetric cryptogram).

But if ciphertext size is an issue, you can use hybrid encryption which gives you minimal ciphertext expansion, and can reduce the cost of deciphering one more password. That's by enciphering all passwords using a symmetric scheme (e.g. AES GCM, which also gives integrity) using the same random key, itself enciphered with an asymmetric scheme. As an additional (marginal) benefit, each server can have its own private key with minimal ciphertext expansion.
Each server needs to store only a single RSA cryptogram (or whatever asymmetric cryptosystem is used), which holds the symmetric key allowing to decipher any password. 

None of this will survive compromise of a server, unless everything sensitive (including RADIUS/CHAP) is in a separate trusted environment, such as an HSM or Smart Card.