What about creating a set of stored procedures for this?

1. User executes "dbo.spuQueueJob @JobName" via OSQL to "manually schedule" the existing job by adding the job name to a queue table.

2. A Scheduled Task runs every 5 minutes (with admin privs) to see if a job was queued via the above proc. If yes, uses sp_start_job for the jobs found in the queue and deletes them from the queue table afterwards.

This way, you do not need to grant the user high privileges. Only the right to execute this dbo.spuQueueJob procedure.