One workaround, suggested by Geoff Streeter, is as follows:
In the source APL:
se←⎕se
)save + tmpse
In the target APL:
)copy ./tmpse se.object
Where se.object is each of the objects which you wish to copy in turn. It would probably be a good idea to generate that list in the original session and save as a variable which could be copied into the target session and used as a base for an automated set of ⎕CYs.
The "+" in )save + causes the interpreter to save a copy of the ⎕SE namespace along with the workspace in an extended workspace file.