BPMN spec allows both messages and signals to carry a payload i.e. some application data; Bizagi BPM Suite does not yet.
It's not a big problem if a message is sent to an intermediate event because it's very easy in Bizagi to write to another process' data and in this scenario the receiving case record is usually known by the sender.
However it is a tough issue if a message is sent to a start event. Let's asume that two cases have sent such messages nearly at the same moment. How can a sender figure out which one of the new cases is it's child? I believe it cannot. This use case may need a payload. Or, as an easy alternative, just a method in the API to get the child process case id and another method to get the record id by a case id. Given those, the sender would be able to write the data into receiver's data space.
As for the signal, it's used to implement a 'loose coupling' between processes. These are scenarios where sender should better not know which process would be responsible for catching the event and vice versa. Therefore writing into other process' data space won't be a good idea for signals -- it'd compromise the idea of loose coupling. So I can't see alternatives to 'true' payload for signals.