The payoff is definitely trust (keeping the old signatures) versus security (strong master key). I can't say which outweighs.
If you continue using the old DSA primary key, all messages encrypted for the new RSA subkey will not be in danger when your DSA key is compromiseds, nor are signatures issued by a new signing subkey. Given usable subkeys are available, they will be used for "day to day" work. The primary key is only used for certification and key management tasks in this case.
This means that an attacker could create new subkeys (which might be automatically picked up for encryption and issue valid signatures, of course!) and revoke the old ones, he could issue certifications, but he cannot read messages encrypted to the RSA subkeys you generated.
I'd go for the second scenario, create a new key pair and issue a certification from your old to your new key. After a time and getting some new certifications on your new key, ditch the old one by revoking it. Consider sending a key transition statement.
When keeping the old DSA masterkey, is it possible to generate an additional new key for signatures?
You can of course add a new signing subkey, but not a subkey for issuing certifications (signatures on keys).