You've hit pretty much all the nails on the head for this. You either need to license a server to your job server, or run it via a foreign call to dtexec, which is only available via windows scheduler if you're not purchasing/installing more software.
There are other scheduling softwares out there that are relatively cheap that you could give the DBA's access to without opening up windows scheduler if you wanted, and they are worth a day or so of investigation just to know what's available.
But, basically, yeah. You're screwed. It's part of the licensing of SQL Server.
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