Drain system for kitchen island

I am remodeling a kitchen in a high rise condo. The sink, disposal, dishwasher will be in a island. A pump system will be required because there is no access trough the concrete floor with a condo unit below and owner will not allow me to tear out their sheet rock ceiling to run plumbing.

I have been able to trench out concrete to run a 1.5 inch pipe from island to a wall where the sink in the old location was connected to a 4" vertical pipe. I had planed on using a under sink sump pump to pump to old drain location. I mistake in this thinking is the venting of sump. Stuttor vent will not work because air needs to go in and out of sump. So venting is my issue.

Any help would be greatly appreciated.

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