I do not think you can do what you want to do. You have a requirement that cannot be fulfilled. Perhaps you can explain the reasons for the requirement.
On the other hand, I was able to have some success several years ago, not with a rexx program, but with an assembler program.
The XCTL is the 'transfer control' macro. In this way, you can have an arbitrary program name, but have it still do IKJEFT01 work. See "MVS Programming: Assembler Services Guide" for more information.
The tricky part is that IKJEFT01 is APF authorized... I think the calling program has to also be APF authorized. Properly protected systems will not allow you to put your load module in an APF data set without a stringent review and approval process.
//MYTSO EXEC PGM=MYTSO,PARM='%MYREXX'
//STEPLIB DD DISP=SHR,DSN=APF.MYTSO.LOAD
Register 1 should continue to point to the original parameter list for more flexibility.
note: if for some reason, you are prohibited from using IKJEFT01 and you try to circumvent the rules, it could be grounds for termination.